Journal articles: 'Symmetric noncommutative spaces'

1

Bekjan, Turdebek N. "Noncommutative Symmetric Hardy Spaces." Integral Equations and Operator Theory 81, no. 2 (December 3, 2014): 191–212. http://dx.doi.org/10.1007/s00020-014-2201-6.

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Sukochev, F. A., and J. Huang. "Isometries on Noncommutative Symmetric Spaces." Doklady Mathematics 103, no. 1 (January 2021): 54–56. http://dx.doi.org/10.1134/s1064562421010129.

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Tulenov, K. S. "Noncommutative vector-valued symmetric Hardy spaces." Russian Mathematics 59, no. 11 (October 15, 2015): 74–79. http://dx.doi.org/10.3103/s1066369x15110092.

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Bekjan, Turdebek N. "Interpolation of noncommutative symmetric martingale spaces." Journal of Operator Theory 77, no. 2 (March 24, 2017): 245–59. http://dx.doi.org/10.7900/jot.2015nov01.2142.

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Jiao, Yong. "Martingale inequalities in noncommutative symmetric spaces." Archiv der Mathematik 98, no. 1 (November 29, 2011): 87–97. http://dx.doi.org/10.1007/s00013-011-0343-1.

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Randrianantoanina, Narcisse, and Lian Wu. "Martingale inequalities in noncommutative symmetric spaces." Journal of Functional Analysis 269, no. 7 (October 2015): 2222–53. http://dx.doi.org/10.1016/j.jfa.2015.05.017.

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Le Merdy, Christian, and Fedor Sukochev. "Rademacher averages on noncommutative symmetric spaces." Journal of Functional Analysis 255, no. 12 (December 2008): 3329–55. http://dx.doi.org/10.1016/j.jfa.2008.05.002.

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Dirksen, Sjoerd, Ben de Pagter, Denis Potapov, and Fedor Sukochev. "Rosenthal inequalities in noncommutative symmetric spaces." Journal of Functional Analysis 261, no. 10 (November 2011): 2890–925. http://dx.doi.org/10.1016/j.jfa.2011.07.015.

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Bekjan, Turdebek N., and Manat Mustafa. "On interpolation of noncommutative symmetric Hardy spaces." Positivity 21, no. 4 (January 17, 2017): 1307–17. http://dx.doi.org/10.1007/s11117-017-0468-y.

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Ma, Congbian, and Youliang Hou. "Quasi-martingale Inequalities in Noncommutative Symmetric Spaces." Bulletin of the Malaysian Mathematical Sciences Society 42, no. 5 (March 28, 2018): 2639–55. http://dx.doi.org/10.1007/s40840-018-0621-1.

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Chilin, Vladimir, and Semyon Litvinov. "Noncommutative weighted individual ergodic theorems with continuous time." Infinite Dimensional Analysis, Quantum Probability and Related Topics 23, no. 02 (June 2020): 2050013. http://dx.doi.org/10.1142/s0219025720500137.

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We show that ergodic flows in the noncommutative [Formula: see text]-space (associated with a semifinite von Neumann algebra) generated by continuous semigroups of positive Dunford–Schwartz operators and modulated by bounded Besicovitch almost periodic functions converge almost uniformly. The corresponding local ergodic theorem is also proved. We then extend these results to arbitrary noncommutative fully symmetric spaces and present applications to noncommutative Orlicz (in particular, noncommutative [Formula: see text]-spaces), Lorentz, and Marcinkiewicz spaces. The commutative counterparts of the results are derived.

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Bergeron, Nantel, Christophe Reutenauer, Mercedes Rosas, and Mike Zabrocki. "Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables." Canadian Journal of Mathematics 60, no. 2 (April 1, 2008): 266–96. http://dx.doi.org/10.4153/cjm-2008-013-4.

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AbstractWe introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions. The bases for this algebra are indexed by set partitions. We show that there exists a natural inclusion of the Hopf algebra of noncommutative symmetric functions in this larger space. We also consider this algebra as a subspace of noncommutative polynomials and use it to understand the structure of the spaces of harmonics and coinvariants with respect to this collection of noncommutative polynomials and conclude two analogues of Chevalley’s theorem in the noncommutative setting.

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Bekjan, Turdebek N. "Duality for symmetric Hardy spaces of noncommutative martingales." Mathematische Zeitschrift 289, no. 3-4 (October 25, 2017): 787–802. http://dx.doi.org/10.1007/s00209-017-1974-0.

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14

Patrick, David. "Noncommutative Symmetric Algebras of Two-Sided Vector Spaces." Journal of Algebra 233, no. 1 (November 2000): 16–36. http://dx.doi.org/10.1006/jabr.2000.8445.

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MA, Congbian, and Guoxi Zhao. "An Interpolation Theorem for Quasimartingales in Noncommutative Symmetric Spaces." Advances in Mathematical Physics 2021 (January 30, 2021): 1–5. http://dx.doi.org/10.1155/2021/6678150.

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Let E be a separable symmetric space on 0 , ∞ and E M the corresponding noncommutative space. In this paper, we introduce a kind of quasimartingale spaces which is like but bigger than E M and obtain the following interpolation result: let E ^ M be the space of all bounded E M -quasimartingales and 1 < p < p E < q E < q < ∞ . Then, there exists a symmetric space F on 0 , ∞ with nontrivial Boyd indices such that E ^ M = L ^ p M , L ^ q M F , K .

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16

Han, Yazhou. "Generalized duality and product of some noncommutative symmetric spaces." International Journal of Mathematics 27, no. 10 (September 2016): 1650082. http://dx.doi.org/10.1142/s0129167x16500828.

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Let [Formula: see text] and [Formula: see text] be two symmetric quasi-Banach spaces and let [Formula: see text] be a semifinite von Neumann algebra. The purpose of this paper is to study the product space [Formula: see text] and the space of multipliers from [Formula: see text] to [Formula: see text], i.e. [Formula: see text]. These spaces share many properties with their classical counterparts. Let [Formula: see text] It is shown that if [Formula: see text] is [Formula: see text]-convex fully symmetric and [Formula: see text] is [Formula: see text]-convex, then [Formula: see text], where [Formula: see text] and [Formula: see text] is the space of multipliers from [Formula: see text] to [Formula: see text] As an application, we give conditions on when [Formula: see text] Moreover, we show that the product space can be described with the help of complex interpolation method.

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17

Sukochev, Fedor, and Dejian Zhou. "2-co-lacunary sequences in noncommutative symmetric Banach spaces." Proceedings of the American Mathematical Society 148, no. 5 (January 13, 2020): 2045–58. http://dx.doi.org/10.1090/proc/14862.

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Chilin, Vladimir, and Fedor Sukochev. "Blum–Hanson type ergodic theorems in noncommutative symmetric spaces." Journal of Functional Analysis 273, no. 1 (July 2017): 329–51. http://dx.doi.org/10.1016/j.jfa.2017.03.011.

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Randrianantoanina, Narcisse, Lian Wu, and Dejian Zhou. "Atomic decompositions and asymmetric Doob inequalities in noncommutative symmetric spaces." Journal of Functional Analysis 280, no. 1 (January 2021): 108794. http://dx.doi.org/10.1016/j.jfa.2020.108794.

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20

HUANG, JINGHAO, GALINA LEVITINA, and FEDOR SUKOCHEV. "M-embedded symmetric operator spaces and the derivation problem." Mathematical Proceedings of the Cambridge Philosophical Society 169, no. 3 (August 20, 2019): 607–22. http://dx.doi.org/10.1017/s030500411900029x.

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AbstractLet ℳ be a semifinite von Neumann algebra with a faithful semifinite normal trace τ. Assume that E(0, ∞) is an M-embedded fully symmetric function space having order continuous norm and is not a superset of the set of all bounded vanishing functions on (0, ∞). In this paper, we prove that the corresponding operator space E(ℳ, τ) is also M-embedded. It extends earlier results by Werner [48, Proposition 4∙1] from the particular case of symmetric ideals of bounded operators on a separable Hilbert space to the case of symmetric spaces (consisting of possibly unbounded operators) on an arbitrary semifinite von Neumann algebra. Several applications are given, e.g., the derivation problem for noncommutative Lorentz spaces ℒp,1(ℳ, τ), 1 < p < ∞, has a positive answer.

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Oussi, Lahcen, and Janusz Wysoczański. "bm-Central Limit Theorems associated with non-symmetric positive cones." Probability and Mathematical Statistics 39, no. 1 (June 10, 2019): 183–97. http://dx.doi.org/10.19195/0208-4147.39.1.12.

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Analogues of the classical Central Limit Theorem are proved in the noncommutative setting of random variables which are bmindependent and indexed by elements of positive non-symmetric cones, such as the circular cone, sectors in Euclidean spaces and the Vinberg cone. The geometry of the cones is shown to play a crucial role and the related volume characteristics of the cones is shown.

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KULA, ANNA, and JANUSZ WYSOCZAŃSKI. "NONCOMMUTATIVE BROWNIAN MOTIONS INDEXED BY PARTIALLY ORDERED SETS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 13, no. 04 (December 2010): 629–61. http://dx.doi.org/10.1142/s021902571000419x.

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We construct noncommutative Brownian motions indexed by partially ordered subsets of Euclidean spaces. The noncommutative independence under consideration is the bm-independence and the time parameter is taken from a positive cone in a vector space ([Formula: see text], the Lorentz cone or the positive definite real symmetric matrices). The construction extends the Muraki's idea of monotonic Brownian motion. We show that our Brownian motions have bm-independent increments for bm-ordered intervals. The appropriate version of the Donsker Invariance Principle is also proved for each positive cone. It requires the bm-Central Limit Theorems related to intervals in the given partially ordered set of indices.

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23

TULENOV, Kanat S., and Madi RAIKHAN. "Outer operators for the noncommutative symmetric hardy spaces associated with finite subdiagonal algebra." Acta Mathematica Scientia 37, no. 3 (May 2017): 799–805. http://dx.doi.org/10.1016/s0252-9602(17)30038-3.

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24

ZAUNER, GERHARD. "QUANTUM DESIGNS: FOUNDATIONS OF A NONCOMMUTATIVE DESIGN THEORY." International Journal of Quantum Information 09, no. 01 (February 2011): 445–507. http://dx.doi.org/10.1142/s0219749911006776.

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This is a one-to-one translation of a German-written Ph.D. thesis from 1999. Quantum designs are sets of orthogonal projection matrices in finite(b)-dimensional Hilbert spaces. A fundamental differentiation is whether all projections have the same rank r, and furthermore the special case r = 1, which contains two important subclasses: Mutually unbiased bases (MUBs) were introduced prior to this thesis and solutions of b + 1 MUBs whenever b is a power of a prime were already given. Unaware of those papers, this concept was generalized here under the notation of regular affine quantum designs. Maximal solutions are given for the general case r ≥ 1, consisting of r(b2 - 1)/(b - r) so-called complete orthogonal classes whenever b is a power of a prime. For b = 6, an infinite family of MUB triples was constructed and it was — as already done in the author's master's thesis (1991) — conjectured that four MUBs do not exist in this dimension. Symmetric informationally complete positive operator-valued measures (SIC POVMs) in this paper are called regular quantum 2-designs with degree 1. The assigned vectors span b2 equiangular lines. These objects had been investigated since the 1960s, but only a few solutions were known in complex vector spaces. In this thesis further maximal analytic and numerical solutions were given (today a lot more solutions are known) and it was (probably for the first time) conjectured that solutions exist in any dimension b (generated by the Weyl–Heisenberg group and with a certain additional symmetry of order 3).

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LEHNER, FRANZ. "CUMULANTS IN NONCOMMUTATIVE PROBABILITY THEORY III: CREATION AND ANNIHILATION OPERATORS ON FOCK SPACES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 08, no. 03 (September 2005): 407–37. http://dx.doi.org/10.1142/s0219025705002049.

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Exchangeability systems arising from Fock space constructions are considered and the corresponding cumulants are computed for generalized Toeplitz operators and similar noncommutative random variables. In particular, simplified calculations are given for the two known examples of q-cumulants. In the second half of the paper we consider in detail the Fock states associated to characters of the infinite symmetric group recently constructed by Bożejko and Guta. We express moments of multidimensional Dyck words in terms of the so-called cycle indicator polynomials of certain digraphs.

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26

Bagchi, Susmit. "Projective and Non-Projective Varieties of Topological Decomposition of Groups with Embeddings." Symmetry 12, no. 3 (March 12, 2020): 450. http://dx.doi.org/10.3390/sym12030450.

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In general, the group decompositions are formulated by employing automorphisms and semidirect products to determine continuity and compactification properties. This paper proposes a set of constructions of novel topological decompositions of groups and analyzes the behaviour of group actions under the topological decompositions. The proposed topological decompositions arise in two varieties, such as decomposition based on topological fibers without projections and decomposition in the presence of translated projections in topological spaces. The first variety of decomposition introduces the concepts of topological fibers, locality of group operation and the partitioned local homeomorphism resulting in formulation of transitions and symmetric surjection within the topologically decomposed groups. The reformation of kernel under decomposed homeomorphism and the stability of group action with the existence of a fixed point are analyzed. The first variety of decomposition does not require commutativity maintaining generality. The second variety of projective topological decomposition is formulated considering commutative as well as noncommutative projections in spaces. The effects of finite translations of topologically decomposed groups under projections are analyzed. Moreover, the embedding of a decomposed group in normal topological spaces is formulated in this paper. It is shown that Schoenflies homeomorphic embeddings preserve group homeomorphism in the decomposed embeddings within normal topological spaces. This paper illustrates that decomposed group embedding in normal topological spaces is separable. The applications aspects as well as parametric comparison of group decompositions based on topology, direct product and semidirect product are included in the paper.

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OECKL, ROBERT. "INTRODUCTION TO BRAIDED QUANTUM FIELD THEORY." International Journal of Modern Physics B 14, no. 22n23 (September 20, 2000): 2461–66. http://dx.doi.org/10.1142/s0217979200001989.

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Indications from various areas of physics point to the possibility that space-time at small scales might not have the structure of a manifold. Noncommutative geometry provides an attractive framework for a perhaps more accurate description of nature. It encompasses the generalisation of spaces to noncommutative spaces and of symmetry groups to quantum groups. This motivates efforts to extend quantum field theory to noncommutative spaces and quantum group symmetries. One also expects that divergences of conventional theories might be regularised in this way.

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Gnatenko, Kh P., and V. M. Tkachuk. "Two-Particle System in Noncommutative Space with Preserved Rotational Symmetry." Ukrainian Journal of Physics 61, no. 5 (May 2016): 432–39. http://dx.doi.org/10.15407/ujpe61.05.0432.

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BLOHMANN, CHRISTIAN. "PERTURBATIVE SYMMETRIES ON NONCOMMUTATIVE SPACES." International Journal of Modern Physics A 19, no. 32 (December 30, 2004): 5693–706. http://dx.doi.org/10.1142/s0217751x04021238.

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Perturbative deformations of symmetry structures on noncommutative spaces are studied in view of noncommutative quantum field theories. The rigidity of enveloping algebras of semisimple Lie algebras with respect to formal deformations is reviewed in the context of star products. It is shown that rigidity of symmetry algebras extends to rigidity of the action of the symmetry on the space. This implies that the noncommutative spaces considered can be realized as star products by particular ordering prescriptions which are compatible with the symmetry. These symmetry preserving ordering prescriptions are calculated for the quantum plane and four-dimensional quantum Euclidean space. The result can be used to construct invariant Lagrangians for quantum field theory on noncommutative spaces with a deformed symmetry.

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Wess, Julius. "q-Deformed Phase Space and its Lattice Structure." International Journal of Modern Physics A 12, no. 28 (November 10, 1997): 4997–5005. http://dx.doi.org/10.1142/s0217751x97002656.

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Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well-defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be interpreted as noncommutative configuration spaces for physical systems. We study the noncommutative Euclidean space that is based on the quantum group SO q(3).

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ARZANO, MICHELE, and DARIO BENEDETTI. "RAINBOW STATISTICS." International Journal of Modern Physics A 24, no. 25n26 (October 20, 2009): 4623–41. http://dx.doi.org/10.1142/s0217751x09045881.

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Noncommutative quantum field theories and their global quantum group symmetries provide an intriguing attempt to go beyond the realm of standard local quantum field theory. A common feature of these models is that the quantum group symmetry of their Hilbert spaces induces additional structure in the multiparticle states which reflects a nontrivial momentum-dependent statistics. We investigate the properties of this "rainbow statistics" in the particular context of κ-quantum fields and discuss the analogies/differences with models with twisted statistics.

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MARTINETTI, PIERRE. "LINE ELEMENT IN QUANTUM GRAVITY: THE EXAMPLE OF DSR AND NONCOMMUTATIVE GEOMETRY." International Journal of Modern Physics A 24, no. 15 (June 20, 2009): 2792–801. http://dx.doi.org/10.1142/s0217751x09046242.

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We question the notion of line element in some quantum spaces that are expected to play a role in quantum gravity, namely noncommutative deformations of Minkowski spaces. We recall how the implementation of the Leibniz rule forbids to see some of the infinitesimal deformed Poincaré transformations as good candidates for Noether symmetries. Then we recall the more fundamental view on the line element proposed in noncommutative geometry, and re-interprete at this light some previous results on Connes' distance formula.

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DIMITRIJEVIĆ, MARIJA, and LARISA JONKE. "TWISTED SYMMETRY AND NONCOMMUTATIVE FIELD THEORY." International Journal of Modern Physics: Conference Series 13 (January 2012): 54–65. http://dx.doi.org/10.1142/s2010194512006733.

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Although the meaning of twisted symmetry is still not fully understood, the twist approach has its advantages in the construction of field theories on noncommutative spaces. We discuss these advantages on the example of κ-Minkowski space-time. We construct the noncommutative U(1) gauge field theory. Especially the action is written as an integral of a maximal form, thus solving the cyclicity problem of the integral in κ-Minkowski. Using the Seiberg-Witten map to relate noncommutative and commutative degrees of freedom the effective action with the first order corrections in the deformation parameter is obtained.

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SINGH, T. P. "STRING THEORY, QUANTUM MECHANICS AND NONCOMMUTATIVE GEOMETRY: A NEW PERSPECTIVE ON THE GRAVITATIONAL DYNAMICS OF D0-BRANES." International Journal of Modern Physics D 15, no. 12 (December 2006): 2153–58. http://dx.doi.org/10.1142/s021827180600973x.

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We do not know the symmetries underlying string theory. Furthermore, there must exist an inherently quantum, and space–time independent, formulation of this theory. Independent of string theory, there should exist a description of quantum mechanics which does not refer to a classical space–time manifold. We propose such a formulation of quantum mechanics, based on noncommutative geometry. This description reduces to standard quantum mechanics, whenever an external classical space–time is available. However, near the Planck energy scale, self-gravity effects modify the Schrödinger equation to the non-linear Doebner–Goldin equation. Remarkably, this non-linear equation also arises in the quantum dynamics of D0-branes. This suggests that the noncommutative quantum dynamics proposed here is actually the quantum gravitational dynamics of D0-branes, and that automorphism invariance is a symmetry of string theory.

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CHAMSEDDINE, ALI H. "COMPLEX GRAVITY AND NONCOMMUTATIVE GEOMETRY." International Journal of Modern Physics A 16, no. 05 (February 20, 2001): 759–66. http://dx.doi.org/10.1142/s0217751x01003883.

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The presence of a constant background antisymmetric tensor for open strings or D-branes forces the space-time coordinates to be noncommutative. An immediate consequence of this is that all fields get complexified. By applying this idea to gravity one discovers that the metric becomes complex. Complex gravity is constructed by gauging the symmetry U(1, D-1). The resulting action gives one specific form of nonsymmetric gravity. In contrast to other theories of nonsymmetric gravity the action is both unique and gauge invariant. It is argued that for this theory to be consistent one must prove the existence of generalized diffeomorphism invariance. The results are easily generalized to noncommutative spaces.

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36

Wang, Simeng. "Quantum symmetries on noncommutative complex spheres with partial commutation relations." Infinite Dimensional Analysis, Quantum Probability and Related Topics 21, no. 04 (December 2018): 1850028. http://dx.doi.org/10.1142/s0219025718500285.

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We introduce the notion of noncommutative complex spheres with partial commutation relations for the coordinates. We compute the corresponding quantum symmetry groups of these spheres, and this yields new quantum unitary groups with partial commutation relations. We also discuss some geometric aspects of the quantum orthogonal groups associated with the mixture of classical and free independence discovered by Speicher and Weber. We show that these quantum groups are quantum symmetry groups on some quantum spaces of spherical vectors with partial commutation relations.

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Bhar, Piyali, and Ayan Banerjee. "Stability of thin-shell wormholes from noncommutative BTZ black hole." International Journal of Modern Physics D 24, no. 05 (March 18, 2015): 1550034. http://dx.doi.org/10.1142/s0218271815500340.

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In this paper, we construct thin-shell wormholes in (2 + 1)-dimensions from noncommutative BTZ black hole by applying the cut-and-paste procedure implemented by Visser. We calculate the surface stresses localized at the wormhole throat by using the Darmois–Israel formalism and we find that the wormholes are supported by matter violating the energy conditions. In order to explore the dynamical analysis of the wormhole throat, we consider that the matter at the shell is supported by dark energy equation of state (EoS) p = ωρ with ω < 0. The stability analysis is carried out of these wormholes to linearized spherically symmetric perturbations around static solutions. Preserving the symmetry we also consider the linearized radial perturbation around static solution to investigate the stability of wormholes which was explored by the parameter β (speed of sound).

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BALACHANDRAN, A. P., and S. KÜRKÇÜOǦLU. "TOPOLOGY CHANGE FOR FUZZY PHYSICS: FUZZY SPACES AS HOPF ALGEBRAS." International Journal of Modern Physics A 19, no. 20 (August 10, 2004): 3395–407. http://dx.doi.org/10.1142/s0217751x04019810.

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Fuzzy spaces are obtained by quantizing adjoint orbits of compact semi-simple Lie groups. Fuzzy spheres emerge from quantizing S2and are associated with the group SU (2) in this manner. They are useful for regularizing quantum field theories and modeling space–times by noncommutative manifolds. We show that fuzzy spaces are Hopf algebras and in fact have more structure than the latter. They are thus candidates for quantum symmetries. Using their generalized Hopf algebraic structures, we can also model processes where one fuzzy space splits into several fuzzy spaces. For example we can discuss the quantum transition where the fuzzy sphere for angular momentum J splits into fuzzy spheres for angular momenta K and L.

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KIM, SANG-WOO, JUN NISHIMURA, and ASATO TSUCHIYA. "CLASSICAL SOLUTIONS IN THE LORENTZIAN MATRIX MODEL FOR SUPERSTRING THEORY." International Journal of Modern Physics: Conference Series 21 (January 2013): 197–99. http://dx.doi.org/10.1142/s2010194513009781.

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Recent Monte Carlo study on the Lorentzian matrix model for superstring theory revealed that an expanding (3 + 1)d universe appears dynamically from (9 + 1)d. The mechanism for the spontaneous breaking of rotational symmetry relies crucially on the noncommutative nature of the three expanding spaces. As a complementary approach to possible future beyond the numerical result, we discuss classical solutions for the Lorentzian matrix model and their properties.

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CASTRO, CARLOS. "THE CLIFFORD SPACE GEOMETRY OF CONFORMAL GRAVITY AND U(4) × U(4) YANG–MILLS UNIFICATION." International Journal of Modern Physics A 25, no. 01 (January 10, 2010): 123–43. http://dx.doi.org/10.1142/s0217751x1004752x.

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It is shown how a conformal gravity and U (4) × U (4) Yang–Mills grand unification model in four dimensions can be attained from a Clifford gauge field theory in C-spaces (Clifford spaces) based on the (complex) Clifford Cl (4, C) algebra underlying a complexified four-dimensional space–time (eight real dimensions). Upon taking a real slice, and after symmetry breaking, it leads to ordinary gravity and the Standard Model in four real dimensions. A brief conclusion about the noncommutative star-product deformations of this Grand Unified Theory of gravity with the other forces of Nature is presented.

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Bhatti, M. Z., Z. Yousaf, and M. Ajmal. "Locally isotropic gravastars with cylindrical spacetime." International Journal of Modern Physics D 28, no. 09 (July 2019): 1950123. http://dx.doi.org/10.1142/s0218271819501232.

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This paper is aimed to set up a thin-shell gravastar model and address its physically accepted features in the background of noncommutative geometry. For this purpose, we have considered the cylindrically symmetric interior metric matched with suitable noncommutative exterior geometry using Israel boundary conditions. The stability of this thin-shell as well as thermodynamical stability is then explored under linear perturbations around the throat. We have found the stable regions near the horizon with some specific values of the involved parameters.

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LIZZI, FEDELE. "STRINGS, NONCOMMUTATIVE GEOMETRY AND THE SIZE OF THE TARGET SPACE." International Journal of Modern Physics A 14, no. 28 (November 10, 1999): 4501–17. http://dx.doi.org/10.1142/s0217751x99002116.

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We describe how the presence of the antisymmetric tensor (torsion) on the world sheet action of string theory renders the size of the target space a gauge noninvariant quantity. This generalizes the R ↔ 1/R symmetry in which momenta and windings are exchanged, to the whole O(d,d,ℤ). The crucial point is that, with a transformation, it is possible always to have all of the lowest eigenvalues of the Hamiltonian to be momentum modes. We interpret this in the framework of noncommutative geometry, in which algebras take the place of point spaces, and of the spectral action principle for which the eigenvalues of the Dirac operator are the fundamental objects, out of which the theory is constructed. A quantum observer, in the presence of many low energy eigenvalues of the Dirac operator (and hence of the Hamiltonian) will always interpreted the target space of the string theory as effectively uncompactified.

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43

Saigo, Hayato. "Category Algebras and States on Categories." Symmetry 13, no. 7 (June 29, 2021): 1172. http://dx.doi.org/10.3390/sym13071172.

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The purpose of this paper is to build a new bridge between category theory and a generalized probability theory known as noncommutative probability or quantum probability, which was originated as a mathematical framework for quantum theory, in terms of states as linear functional defined on category algebras. We clarify that category algebras can be considered to be generalized matrix algebras and that the notions of state on category as linear functional defined on category algebra turns out to be a conceptual generalization of probability measures on sets as discrete categories. Moreover, by establishing a generalization of famous GNS (Gelfand–Naimark–Segal) construction, we obtain a representation of category algebras of †-categories on certain generalized Hilbert spaces which we call semi-Hilbert modules over rigs. The concepts and results in the present paper will be useful for the studies of symmetry/asymmetry since categories are generalized groupoids, which themselves are generalized groups.

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AMELINO-CAMELIA, GIOVANNI. "PROPOSAL OF A SECOND GENERATION OF QUANTUM-GRAVITY-MOTIVATED LORENTZ-SYMMETRY TESTS: SENSITIVITY TO EFFECTS SUPPRESSED QUADRATICALLY BY THE PLANCK SCALE." International Journal of Modern Physics D 12, no. 09 (October 2003): 1633–39. http://dx.doi.org/10.1142/s0218271803004080.

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Over the last few years the study of possible Planck-scale departures from classical Lorentz symmetry has been one of the most active areas of quantum-gravity research. We now have a satisfactory description of the fate of Lorentz symmetry in the most popular noncommutative spacetimes and several studies have been devoted to the fate of Lorentz symmetry in loop quantum gravity. Remarkably there are planned experiments with enough sensitivity to reveal these quantum-spacetime effects, if their magnitude is only linearly suppressed by the Planck length. Unfortunately, in some quantum-gravity scenarios even the strongest quantum-spacetime effects are suppressed by at least two powers of the Planck length, and many authors have argued that it would be impossible to test these quadratically-suppressed effects. I here observe that advanced cosmic-ray observatories and neutrino observatories can provide the first elements of an experimental programme testing the possibility of departures from Lorentz symmetry that are quadratically Planck-length suppressed.

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Arzano, Michele, and Tomasz Trześniewski. "Space-Time Defects and Group Momentum Space." Advances in High Energy Physics 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/4731050.

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We study massive and massless conical defects in Minkowski and de Sitter spaces in various space-time dimensions. The energy momentum of a defect, considered as an (extended) relativistic object, is completely characterized by the holonomy of the connection associated with its space-time metric. The possible holonomies are given by Lorentz group elements, which are rotations and null rotations for massive and massless defects, respectively. In particular, if we fix the direction of propagation of a massless defect in n+1-dimensional Minkowski space, then its space of holonomies is a maximal Abelian subgroup of the AN(n-1) group, which corresponds to the well known momentum space associated with the n-dimensional κ-Minkowski noncommutative space-time and κ-deformed Poincaré algebra. We also conjecture that massless defects in n-dimensional de Sitter space can be analogously characterized by holonomies belonging to the same subgroup. This shows how group-valued momenta related to four-dimensional deformations of relativistic symmetries can arise in the description of motion of space-time defects.

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Murray, Seán, and Jan Govaerts. "Noncommutative spherically symmetric spaces." Physical Review D 83, no. 2 (January 10, 2011). http://dx.doi.org/10.1103/physrevd.83.025009.

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Burić, Maja, and John Madore. "On noncommutative spherically symmetric spaces." European Physical Journal C 74, no. 3 (March 2014). http://dx.doi.org/10.1140/epjc/s10052-014-2820-8.

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Bieliavsky, Pierre, Razvan Gurau, and Vincent Rivasseau. "Noncommutative field theory on rank one symmetric spaces." Journal of Noncommutative Geometry, 2009, 99–123. http://dx.doi.org/10.4171/jncg/32.

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Bekjan, Turdebek N., and Myrzagali N. Ospanov. "On products of noncommutative symmetric quasi Banach spaces and applications." Positivity, April 9, 2020. http://dx.doi.org/10.1007/s11117-020-00753-x.

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Bekjan, Turdebek N., Zeqian Chen, Madi Raikhan, and Mu Sun. "Interpolation and the John–Nirenberg inequality on symmetric spaces of noncommutative martingales." Studia Mathematica, 2021. http://dx.doi.org/10.4064/sm200508-11-12.

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Journal articles on the topic 'Symmetric noncommutative spaces'

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