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Journal articles on the topic 'Commutator theory'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

Chekhlov, Andrey R., and Peter V. Danchev. "On commutator Krylov transitive and commutator weakly transitive Abelian p-groups." Forum Mathematicum 31, no. 6 (November 1, 2019): 1607–23. http://dx.doi.org/10.1515/forum-2019-0066.

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AbstractWe define the concepts of commutator (Krylov) transitive and strongly commutator (Krylov) transitive Abelian p-groups. These two innovations are respectively non-trivial generalizations of the notions of commutator fully transitive and strongly commutator fully transitive p-groups from a paper of Chekhlov and Danchev (J. Group Theory, 2015). They are also commutator socle-regular in the sense of Danchev and Goldsmith (J. Group Theory, 2014). Various results from there and from a paper of Goldsmith and Strüngmann (Houston J. Math., 2007) are considerably extended to this new point of view. We also define and explore the concept of a commutator weakly transitive Abelian p-group, comparing its properties with those of the aforementioned two group classes. Some affirmations, sounding quite curiously, are detected in order to illustrate the pathology of the commutators in the endomorphism rings of p-primary Abelian groups.

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2

FINKELSTEIN, ROBERT J. "q GAUGE THEORY." International Journal of Modern Physics A 11, no. 04 (February 10, 1996): 733–46. http://dx.doi.org/10.1142/s0217751x9600033x.

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We examine some issues that arise in the q deformation of a gauge theory. If the deformation is carried out by replacing the equal time commutators of free fields with the corresponding q commutators, the resulting propagators are not very much different from those of the undeformed theory as long as one is dealing with weak fields; but the theory still violates causality. If one postulates a q-deformed S matrix, the corresponding q causal commutator has two poles of different strength and the result again amounts to a deformation of the Lorentz group.

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3

Acciarri, Cristina, and Pavel Shumyatsky. "Commutators and commutator subgroups in profinite groups." Journal of Algebra 473 (March 2017): 166–82. http://dx.doi.org/10.1016/j.jalgebra.2016.11.001.

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4

Carro, María J. "Commutators and analytic families of operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 129, no. 4 (1999): 685–96. http://dx.doi.org/10.1017/s030821050001307x.

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This work connects the theory of commutators with analytic families of operators in abstract interpolation theory. Our main result asserts that if {Lξ}0≤Reξ≤1 is an analytic family of operators satisfying some conditions, then [Lθ,Ω] +(Lξ)′(θ): Āθ→ Bθ is bounded. From this, we can deduce the boundedness of the commutator .

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5

Kaushik, Rahul, and Manoj K. Yadav. "Commutators and commutator subgroups of finite p-groups." Journal of Algebra 568 (February 2021): 314–48. http://dx.doi.org/10.1016/j.jalgebra.2020.10.007.

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6

Stanovský, David, and Petr Vojtěchovský. "Commutator theory for loops." Journal of Algebra 399 (February 2014): 290–322. http://dx.doi.org/10.1016/j.jalgebra.2013.08.045.

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7

Faizal, Mir. "Deformation of second and third quantization." International Journal of Modern Physics A 30, no. 09 (March 25, 2015): 1550036. http://dx.doi.org/10.1142/s0217751x15500360.

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In this paper, we will deform the second and third quantized theories by deforming the canonical commutation relations in such a way that they become consistent with the generalized uncertainty principle. Thus, we will first deform the second quantized commutator and obtain a deformed version of the Wheeler–DeWitt equation. Then we will further deform the third quantized theory by deforming the third quantized canonical commutation relation. This way we will obtain a deformed version of the third quantized theory for the multiverse.

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8

Lipparini, Paolo. "Commutator theory without join-distributivity." Transactions of the American Mathematical Society 346, no. 1 (January 1, 1994): 177–202. http://dx.doi.org/10.1090/s0002-9947-1994-1257643-7.

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9

Robinson, Derek W. "Commutator Theory on Hilbert Space." Canadian Journal of Mathematics 39, no. 5 (October 1, 1987): 1235–80. http://dx.doi.org/10.4153/cjm-1987-063-2.

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Commutator theory has its origins in constructive quantum field theory. It was initially developed by Glirnm and Jaffe [7] as a method to establish self-adjointness of quantum fields and model Hamiltonians. But it has subsequently proved useful for a variety of other problems in field theory [17] [15] [8] [3], quantum mechanics [5], and Lie group theory [6]. Despite all these detailed applications no attempt appears to have been made to systematically develop the theory although reviews have been given in [22] and [9]. The primary aim of the present paper is to partially correct this situation. The secondary aim is to apply the theory to the analysis of first and second order partial differential operators associated with a Lie group.

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10

Pedicchio, M. C. "Arithmetical categories and commutator theory." Applied Categorical Structures 4, no. 2-3 (1996): 297–305. http://dx.doi.org/10.1007/bf00122258.

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11

KIM, WON TAE, and JOHN J. OH. "NONCOMMUTATIVE OPEN STRINGS FROM DIRAC QUANTIZATION." Modern Physics Letters A 15, no. 26 (August 30, 2000): 1597–604. http://dx.doi.org/10.1142/s0217732300002127.

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We study Dirac commutators of canonical variables on D-branes with a constant Neveu–Schwarz two-form field by using the Dirac constraint quantization method, and point out some subtleties appearing in previous works in analyzing constraint structure of the brane system. Overcoming some ad hoc procedures, we obtain desirable noncommutative coordinates exactly compatible with the result of the conformal field theory in recent literatures. Furthermore, we find interesting commutator relations of other canonical variables.

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12

Germain, Emmanuel. "K-Theory of the Commutator Ideal." K-Theory 23, no. 1 (May 2001): 41–52. http://dx.doi.org/10.1023/a:1017564222199.

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13

Kearnes, Keith, and Ralph McKenzie. "Commutator theory for relatively modular quasivarieties." Transactions of the American Mathematical Society 331, no. 2 (February 1, 1992): 465–502. http://dx.doi.org/10.1090/s0002-9947-1992-1062872-x.

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14

Pedicchio, M. C. "A Categorical Approach to Commutator Theory." Journal of Algebra 177, no. 3 (November 1995): 647–57. http://dx.doi.org/10.1006/jabr.1995.1321.

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15

PLACHTA, L. "Cn-MOVES, BRAID COMMUTATORS AND VASSILIEV KNOT INVARIANTS." Journal of Knot Theory and Its Ramifications 13, no. 06 (September 2004): 809–28. http://dx.doi.org/10.1142/s0218216504003469.

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We show that for each positive integer n>1 a simple Cn-move on knots, introduced by Habiro, is equivalent to the (non-oriented) insertion in a knot via a tangle map the geometric pure braid n-commutator of the form pn=[pn-1,n,[pn-2,n-1,…, [p1,2,p0,1]…]∈Pn+1, where Pn+1 is the subgroup of pure braids of the braid group Bn+1 on n+1 strands. We relate the insertions of the pure braid commutators in knots to the operations of inverting and mirroring the knots.

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16

LUO, LIN, WEN-XIU MA, and EN-GUI FAN. "THE ALGEBRAIC STRUCTURE OF ZERO CURVATURE REPRESENTATIONS ASSOCIATED WITH INTEGRABLE COUPLINGS." International Journal of Modern Physics A 23, no. 09 (April 10, 2008): 1309–25. http://dx.doi.org/10.1142/s0217751x08039347.

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The commutator of enlarged vector fields was explicitly computed for integrable coupling systems associated with semidirect sums of Lie algebras. An algebraic structure of zero curvature representations is then established for such integrable coupling systems. As an application example of this algebraic structure, the commutation relations of Lax operators corresponding to the enlarged isospectral and nonisospectral AKNS flows are worked out, and thus a τ-symmetry algebra for the AKNS integrable couplings is engendered from this theory.

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17

Mehdi-Nezhad, Elham, and Amir M. Rahimi. "The annihilation graphs of commutator posets and lattices with respect to an element." Journal of Algebra and Its Applications 16, no. 06 (April 12, 2017): 1750106. http://dx.doi.org/10.1142/s0219498817501067.

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We propose a new, widely generalized context for the study of the zero-divisor type (annihilating-ideal) graphs, where the vertices of graphs are not elements/ideals of a commutative ring, but elements of an abstract ordered set [lattice] (imitating the lattice of ideals of a ring), equipped with a commutative (not necessarily associative) binary operation (imitating the product of ideals of a ring). We discuss, when [Formula: see text] (the annihilation graph of the commutator poset [lattice] [Formula: see text] with respect to an element [Formula: see text]) is a complete bipartite graph together with some of its other graph-theoretic properties. In contrast to the case of rings, we construct a commutator poset whose [Formula: see text] contains a cut-point. We provide some examples to show that some conditions are not superfluous assumptions. We also give some examples of a large class of lattices, such as the lattice of ideals of a commutative ring, the lattice of normal subgroups of a group, and the lattice of all congruences on an algebra in a variety (congruence modular variety) by using the commutators as the multiplicative binary operation on these lattices. This shows that how the commutator theory can define and unify many zero-divisor type graphs of different algebraic structures as a special case of this paper.

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18

Nakazi, Takahiko. "Commutator of two projections in prediction theory." Bulletin of the Australian Mathematical Society 34, no. 1 (August 1986): 65–71. http://dx.doi.org/10.1017/s0004972700004500.

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Let w be a nonnegative weight function in L1 = L1 (dθ/2π). Let Q and P denote the orthogonal projections to the closed linear spans in L2(wdθ/2π) of {einθ: n ≤ 0} and {einθ: n > 0}, respectively. The commutator of Q and P is studied. This has applications for prediction problems when such a weight arises as the spectral density of a discrete weakly stationary Gaussian stochastic process.

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19

Moorhead, Andrew. "Higher commutator theory for congruence modular varieties." Journal of Algebra 513 (November 2018): 133–58. http://dx.doi.org/10.1016/j.jalgebra.2018.07.026.

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20

Golénia, Sylvain, and Thierry Jecko. "A New Look at Mourre’s Commutator Theory." Complex Analysis and Operator Theory 1, no. 3 (April 2, 2007): 399–422. http://dx.doi.org/10.1007/s11785-007-0011-4.

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21

Everaert, Tomas, and Tim Van der Linden. "Relative commutator theory in semi-abelian categories." Journal of Pure and Applied Algebra 216, no. 8-9 (August 2012): 1791–806. http://dx.doi.org/10.1016/j.jpaa.2012.02.018.

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22

Cigoli, Alan S., Arnaud Duvieusart, Marino Gran, and Sandra Mantovani. "Galois theory and the categorical Peiffer commutator." Homology, Homotopy and Applications 22, no. 2 (2020): 323–46. http://dx.doi.org/10.4310/hha.2020.v22.n2.a20.

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23

AGHABALI, M., S. AKBARI, M. ARIANNEJAD, and A. MADADI. "VECTOR SPACE GENERATED BY THE MULTIPLICATIVE COMMUTATORS OF A DIVISION RING." Journal of Algebra and Its Applications 12, no. 08 (July 31, 2013): 1350043. http://dx.doi.org/10.1142/s0219498813500436.

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Let D be a division ring with center F. An element of the form xyx-1y-1 ∈ D is called a multiplicative commutator. Let T(D) be the vector space over F generated by all multiplicative commutators in D. In this paper it is shown that if D is algebraic over F and Char (D) = 0, then D = T(D). We conjecture that it is true in general. Among other results it is shown that in characteristic zero if T(D) is algebraic over F, then D is algebraic over F.

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24

Baddeley, Robert W. "Images of commutator MAPS." Communications in Algebra 22, no. 8 (January 1994): 3023–35. http://dx.doi.org/10.1080/00927879408825010.

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25

Pulmannová, Sylvia. "Commutator-Finite D-Lattices." Order 21, no. 2 (May 2004): 91–105. http://dx.doi.org/10.1007/s11083-004-5257-0.

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26

Greechie, Richard, and Louis Herman. "Commutator-finite orthomodular lattices." Order 1, no. 3 (1985): 277–84. http://dx.doi.org/10.1007/bf00383604.

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27

Isidro, J. M., P. Fernández de Córdoba, J. M. Rivera-Rebolledo, and J. L. G. Santander. "Remarks on the Representation Theory of the Moyal Plane." Advances in Mathematical Physics 2011 (2011): 1–9. http://dx.doi.org/10.1155/2011/635790.

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28

Barrenechea, A. L. "Shift commutator algebras and multipliers." Filomat 32, no. 17 (2018): 5837–43. http://dx.doi.org/10.2298/fil1817837b.

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We determine the precise structure of all multipliers on the commutator algebra associated to the shift operator on a Hilbert space. The problem has its own interest by its connection with the theory of Toeplitz and Laurent operators.

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29

LI, TIANJUN, YAN LIU, and DAN XIE. "MULTIPLE D2-BRANE ACTION FROM M2-BRANES." International Journal of Modern Physics A 24, no. 16n17 (July 10, 2009): 3039–52. http://dx.doi.org/10.1142/s0217751x09044590.

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We study the detailed derivation of the multiple D2-brane effective action from multiple M2-branes in the Bagger–Lambert–Gustavsson (BLG) theory and the Aharony–Bergman–Jafferis–Maldacena (ABJM) theory by employing the novel Higgs mechanism. We show explicitly that the high-order F3 and F4 terms are commutator terms, and conjecture that all the high-order terms are commutator terms. Because the commutator terms can be treated as the covariant derivative terms, these high-order terms do not contribute to the multiple D2-brane effective action. Inspired by the derivation of a single D2-brane from a M2-brane, we consider the curved M2-branes and introduce an auxiliary field. Integrating out the auxiliary field, we indeed obtain the correct high-order F4 terms in the D2-brane effective action from the BLG theory and the ABJM theory with SU(2) × SU(2) gauge symmetry, but we cannot obtain the correct high-order F4 terms from the ABJM theory with U(N) × U(N) and SU(N) × SU(N) gauge symmetries for N > 2. We also briefly comment on the (gauged) BF membrane theory.

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30

Burris, Stanley. "Book Review: Commutator theory for congruence modular varieties." Bulletin of the American Mathematical Society 20, no. 1 (January 1, 1989): 94–97. http://dx.doi.org/10.1090/s0273-0979-1989-15710-8.

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31

Everaert, T. "Relative commutator theory in varieties of Ω-groups." Journal of Pure and Applied Algebra 210, no. 1 (July 2007): 1–10. http://dx.doi.org/10.1016/j.jpaa.2006.05.011.

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32

Cheng, Che-Man, and Yaru Liang. "Singular Values, Eigenvalues and Diagonal Elements Of The Commutator Of 2x2 Rank One Matrices." Electronic Journal of Linear Algebra 36, no. 36 (January 20, 2020): 1–20. http://dx.doi.org/10.13001/ela.2020.4955.

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We determine the region of singular values of the commutator XY-YX for 2x2 rank one complex matrices X and Y. This answers in affirmative a conjecture raised in [Wenzel 2015] when 2x2 matrices are concerned. Our approach and proofs also lead to a complete relation between the singular values, eigenvalues and diagonal elements of the commutator under consideration.

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33

Yokoyama, Koichiro. "Mourre theory for time-periodic systems." Nagoya Mathematical Journal 149 (March 1998): 193–210. http://dx.doi.org/10.1017/s0027763000006607.

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Abstract.Studies for A.C. Stark Hamiltonian are closely related to that for the self-adjoint operator on torus. In this paper we use Mourre’s commutator method, which makes great progress for the study of time-independent Hamiltonian. By use of it we show the asymptotic behavior of the unitary propagator as σ → ± ∞.

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34

TÜRKAY, Merve Esra. "Some New Estimates for Maximal Commutator and Commutator of Maximal Function in $L_{p,\lambda}(\Gamma)$." Journal of New Theory, no. 40 (September 30, 2022): 74–81. http://dx.doi.org/10.53570/jnt.1162966.

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The theory of boundedness of classical operators of real analyses on Morrey spaces defined on Carleson curves has made significant progress in recent years as it allows for various applications. This study obtains new estimates about the boundedness of the maximal commutator operator $M_b$ and the commutator of the maximal function $[M, b]$ in Morrey spaces defined on Carleson curves.

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35

R, Iyer. "Proof Formalism General Quantum Density Commutator Matrix Physics." Physical Science & Biophysics Journal 5, no. 2 (2021): 1–5. http://dx.doi.org/10.23880/psbj-16000185.

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Formalism proofing general derivation, applying matrix properties operations, showing fundamental relationships with inner product to outer product has been advanced here. This general proof formalism has direct application with physics to quantify quantum density at micro scale level to time commutator at macro scale level. System of operator algebraic equations has been rigorously derived to obtain analytic solutions which are physically acceptable. Extended physics application will include metricizing towards unitarization to achieve gaging Hamiltonian mechanics to electromagnetic gravitational strong theory, towards grand unifying physics atomistic to astrophysics or vice versa via quantum relativistic general physics thereby patching to classical physics fields energy.

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36

Bremner, Murray. "Identities for the Ternary Commutator." Journal of Algebra 206, no. 2 (August 1998): 615–23. http://dx.doi.org/10.1006/jabr.1998.7433.

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37

Robinson, Geoffrey R. "Characters and the commutator map." Journal of Algebra 321, no. 11 (June 2009): 3521–26. http://dx.doi.org/10.1016/j.jalgebra.2008.02.032.

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38

Day, A., and H. P. Gumm. "Some characterizations of the commutator." Algebra Universalis 29, no. 1 (March 1992): 61–78. http://dx.doi.org/10.1007/bf01190756.

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39

Hoover, Melissa Meehan. "Symplectic commutator subgroups." Linear Algebra and its Applications 423, no. 2-3 (June 2007): 305–23. http://dx.doi.org/10.1016/j.laa.2007.01.002.

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40

POLYAKOV, DIMITRI. "(NON)TRIVIALITY OF PURE SPINORS AND EXACT PURE SPINOR–RNS MAP." International Journal of Modern Physics A 24, no. 14 (June 10, 2009): 2677–87. http://dx.doi.org/10.1142/s0217751x09043250.

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All the BRST-invariant operators in pure spinor formalism in d = 10 can be represented as BRST commutators, such as [Formula: see text] where λ+ is the U(5) component of the pure spinor transforming as [Formula: see text]. Therefore, in order to secure nontriviality of BRST cohomology in pure spinor string theory, one has to introduce "small Hilbert space" and "small operator algebra" for pure spinors, analogous to those existing in RNS formalism. As any invariant vertex operator in RNS string theory can also represented as a commutator V = {Q brst , LV} where L = -4c∂ξξe-2ϕ, we show that mapping [Formula: see text] to L leads to identification of the pure spinor variable λα in terms of RNS variables without any additional nonminimal fields. We construct the RNS operator satisfying all the properties of λα and show that the pure spinor BRST operator ∮λαdα is mapped (up to similarity transformation) to the BRST operator of RNS theory under such a construction.

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41

Pressman, Irwin S. "Generalized Commutators and the Moore-Penrose Inverse." Electronic Journal of Linear Algebra 37 (September 27, 2021): 598–612. http://dx.doi.org/10.13001/ela.2021.4991.

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This work studies the kernel of a linear operator associated with the generalized k-fold commutator. Given a set $\mathfrak{A}= \left\{ A_{1}, \ldots ,A_{k} \right\}$ of real $n \times n$ matrices, the commutator is denoted by$[A_{1}| \ldots |A_{k}]$. For a fixed set of matrices $\mathfrak{A}$ we introduce a multilinear skew-symmetric linear operator $T_{\mathfrak{A}}(X)=T(A_{1}, \ldots ,A_{k})[X]=[A_{1}| \ldots |A_{k} |X] $. For fixed $n$ and $k \ge 2n-1, \; T_{\mathfrak{A}} \equiv 0$ by the Amitsur--Levitski Theorem [2] , which motivated this work. The matrix representation $M$ of the linear transformation $T$ is called the k-commutator matrix. $M$ has interesting properties, e.g., it is a commutator; for $k$ odd, there is a permutation of the rows of $M$ that makes it skew-symmetric. For both $k$ and $n$ odd, a provocative matrix $\mathcal{S}$ appears in the kernel of $T$. By using the Moore--Penrose inverse and introducing a conjecture about the rank of $M$, the entries of $\mathcal{S}$ are shown to be quotients of polynomials in the entries of the matrices in $\mathfrak{A}$. One case of the conjecture has been recently proven by Brassil. The Moore--Penrose inverse provides a full rank decomposition of $M$.

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42

ACCARDI, LUIGI, and YUJI HIBINO. "CANONICAL REPRESENTATION OF STATIONARY QUANTUM GAUSSIAN PROCESSES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 05, no. 03 (September 2002): 421–28. http://dx.doi.org/10.1142/s0219025702000869.

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Stimulated by the quantum generalization of the canonical representation theory for Gaussian processes in Ref. 1, we first give the representations (not necessarily canonical) of two stationary Gaussian processes X and Y by means of white noises qt and pt with no assumptions on their commutator. We then assume that qt + ipt annihilates the vacuum state and prove that the representations are the joint Boson–Fock ones if and only if X and Y have a scalar commutator.

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43

Vakulenko, A. F. "On a variant of commutator estimates in spectral theory." Journal of Soviet Mathematics 49, no. 5 (May 1990): 1136–39. http://dx.doi.org/10.1007/bf02208709.

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44

Jo, S. "Commutator of gauge generators in non-abelian chiral theory." Nuclear Physics B 259, no. 4 (September 1985): 616–36. http://dx.doi.org/10.1016/0550-3213(85)90004-5.

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45

Chiş, Mihai. "Another characterization of the commutator subgroup." Communications in Algebra 20, no. 12 (January 1992): 3781–84. http://dx.doi.org/10.1080/00927879208824542.

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46

Sapir, Olga. "Levi’s Commutator Theorems for Cancellative Semigroups." Semigroup Forum 71, no. 1 (August 25, 2005): 140–46. http://dx.doi.org/10.1007/s00233-004-0178-1.

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47

Padmanabhan, R., W. McCune, and R. Veroff. "Levi’s Commutator Theorems for Cancellative Semigroups." Semigroup Forum 71, no. 1 (August 25, 2005): 152–57. http://dx.doi.org/10.1007/s00233-005-0506-0.

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48

Semyonov, Yu S. "Commutator subgroups of irreducible C-group." Sbornik: Mathematics 187, no. 3 (April 30, 1996): 403–12. http://dx.doi.org/10.1070/sm1996v187n03abeh000118.

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49

Letzter, Edward S. "Commutator Hopf Subalgebras and Irreducible Representations." Communications in Algebra 35, no. 7 (June 15, 2007): 2183–90. http://dx.doi.org/10.1080/00927870701302198.

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50

Kiss, Emil W. "Three remarks on the modular commutator." Algebra Universalis 29, no. 4 (December 1992): 455–76. http://dx.doi.org/10.1007/bf01190773.

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