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Relevant bibliographies by topics / Tomita algebras

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Academic literature on the topic 'Tomita algebras'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 February 2022

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Journal articles on the topic "Tomita algebras"

1

BORCHERS, H. J., and JAKOB YNGVASON. "TRANSITIVITY OF LOCALITY AND DUALITY IN QUANTUM FIELD THEORY." Reviews in Mathematical Physics 06, no. 04 (August 1994): 597–619. http://dx.doi.org/10.1142/s0129055x94000201.

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Duality conditions for Wightman fields are formulated in terms of the Tomita conjugations S associated with algebras of unbounded operators. It is shown that two fields which are relatively local to an irreducible field fulfilling a condition of this type are relatively local to each other. Moreover, a local net of von Neumann algebras associated with such a field satisfies (essential) duality. These results do not rely on Lorentz covariance but follow from the observation that two algebras of (un)bounded operators with the same Tomita conjugation have the same (un)bounded weak commutant if one algebra is contained in the other.

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Nikolaev, Igor V. "On ClusterC⁎-Algebras." Journal of Function Spaces 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/9639875.

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We introduce aC⁎-algebraA(x,Q)attached to the clusterxand a quiverQ. IfQTis the quiver coming from triangulationTof the Riemann surfaceSwith a finite number of cusps, we prove that the primitive spectrum ofA(x,QT)timesRis homeomorphic to a generic subset of the Teichmüller space of surfaceS. We conclude with an analog of the Tomita-Takesaki theory and the Connes invariantT(M)for the algebraA(x,QT).

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3

Frank, Michael. "Elements of Tomita-Takesaki theory for embeddable AW*-algebras." Annals of Global Analysis and Geometry 7, no. 2 (1989): 115–31. http://dx.doi.org/10.1007/bf00127862.

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4

Shulman, Victor S. "Quasivectors and Tomita–Takesaki Theory for Operator Algebras on Π1-Spaces." Reviews in Mathematical Physics 09, no. 06 (August 1997): 749–83. http://dx.doi.org/10.1142/s0129055x97000270.

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We consider operator algebras, which are symmetric with respect to an indefinite scalar product. It is shown, that in the case when the rank of indefiniteness is equal to 1 there exists a working modular theory, and in particular a precise analogue of the Fundamental Tomita's Theorem holds: For any weakly closed J-symmetric operator algebra [Formula: see text] with identity on a Π1-space H which has a cyclic and separating vector, there is an antilinear J-involution j : H→H such that [Formula: see text]. The paper also contains a full proof of the Double Commutant Theorem for J-symmetric operator algebras on Π1-spaces.

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5

Thaheem, A. B. "On certain decompositional properties of von Neumann algebras." Glasgow Mathematical Journal 29, no. 2 (July 1987): 177–79. http://dx.doi.org/10.1017/s0017089500006819.

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It is well known that if α and β are commuting *-automorphisms of a von Neumann algebra M satisfying the equation α + α-1 = β + β-1 then M can be decomposed into a direct sum of subalgebras Mp and M(l − p) by a central projection p in M such that α = β on Mp and α = β-1 on M(1 − p) (see, for instance, [6], [7], [2]). Originally this equation arose in the Tomita-Takesaki theory (see, for example, [11]) in the form of one-parameter modular automorphism groups and later on it has been studied for arbitrary automorphisms and one-parameter groups of automorphisms on von Neumann algebras [7], [8], [9]. In the case of automorphism groups satisfying the above equation, one has a similar decomposition but this time without assuming the commutativity condition (cf. [7], [8]). For another relevant work on one-parameter groups of automorphisms which is close to our papers [7] and [8], we refer to Ciorănescu and Zsidó [1]. Regarding applications, this equation has been used for arbitrary automorphisms in the geometric interpretation of the Tomita-Takesaki theory [2] and in the case of automorphism groups it has been a fundamental tool in the generalization of the Tomita-Takesaki theory to Jordan algebras [3]. We may remark that the decomposition in the commuting case [6], [7] is much simpler than in the case of automorphism groups in the non-commutative situation [8]. In some cases one can obtain the decomposition for an arbitrary pair of automorphisms without assuming their commutativity but the problem in the general case has been unresolved. Recently we have shown that if α and β are *-automorphisms of a von Neumann algebra M satisfying the equation α + α-1 = β + β-1 (without assuming the commutativity of α and β) then there exists a central projection p in M such that α2= β2 on Mp and α2 = β−2 on M(l − p) [10].

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Neto, A. Matos, A. E. Santana, J. D. M. Vianna, and F. C. Khanna. "The Tomita‐Takesaki Representation ofw*‐Algebras, Lie Groups, and Thermofield Dynamics." Physics Essays 9, no. 4 (December 1996): 596–603. http://dx.doi.org/10.4006/1.3029276.

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7

Popescu, Gelu. "!COMMUTANT LIFTING, TENSOR ALGEBRAS, AND FUNCTIONAL CALCULUS." Proceedings of the Edinburgh Mathematical Society 44, no. 2 (June 2001): 389–406. http://dx.doi.org/10.1017/s0013091598001059.

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AbstractA non-commutative multivariable analogue of Parrott’s generalization of the Sz.-Nagy–Foia\c{s} commutant lifting theorem is obtained. This yields Tomita-type commutant results and interpolation theorems (e.g. Sarason, Nevanlinna–Pick, Carathéodory) for $F_n^\infty\,\bar{\otimes}\,\M$, the weakly-closed algebra generated by the spatial tensor product of the non-commutative analytic Toeplitz algebra $F_n^\infty$ and an arbitrary von Neumann algebra $\M$. In particular, we obtain interpolation theorems for bounded analytic functions from the open unit ball of $\mathbb{C}^n$ into a von Neumann algebra.A variant of the non-commutative Poisson transform is used to extend the von Neumann inequality to tensor algebras, and to provide a generalization of the functional calculus for contractive sequences of operators on Hilbert spaces. Commutative versions of these results are also considered.AMS 2000 Mathematics subject classification: Primary 47L25; 47A57; 47A60. Secondary 30E05

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BRUNETTI, R., D. GUIDO, and R. LONGO. "MODULAR LOCALIZATION AND WIGNER PARTICLES." Reviews in Mathematical Physics 14, no. 07n08 (July 2002): 759–85. http://dx.doi.org/10.1142/s0129055x02001387.

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We propose a framework for the free field construction of algebras of local observables which uses as an input the Bisognano–Wichmann relations and a representation of the Poincaré group on the one-particle Hilbert space. The abstract real Hilbert subspace version of the Tomita–Takesaki theory enables us to bypass some limitations of the Wigner formalism by introducing an intrinsic spacetime localization. Our approach works also for continuous spin representations to which we associate a net of von Neumann algebras on spacelike cones with the Reeh–Schlieder property. The positivity of the energy in the representation turns out to be equivalent to the isotony of the net, in the spirit of Borchers theorem. Our procedure extends to other spacetimes homogeneous under a group of geometric transformations as in the case of conformal symmetries and of de Sitter spacetime.

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9

Scholberg, Johannes, Brian L. McNeal, James W. Jones, Kenneth J. Boote, Craig D. Stanley, and Thomas A. Obreza. "Growth and Canopy Characteristics of Field-Grown Tomato." Agronomy Journal 92, no. 1 (2000): 152. http://dx.doi.org/10.1007/s100870050017.

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10

Thönnissen, Carmen, David J. Midmore, Jagdish K. Ladha, Robert J. Holmer, and Urs Schmidhalter. "Tomato Crop Response to Short-Duration Legume Green Manures in Tropical Vegetable Systems." Agronomy Journal 92, no. 2 (2000): 245. http://dx.doi.org/10.1007/s100870050029.

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Dissertations / Theses on the topic "Tomita algebras"

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Semplice, Matteo. "Boundary conformal fields and Tomita-Takesaki theory." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270734.

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Tedesco, Gennaro. "Modular structure of chiral Fermi fields in conformal quantum field theory." Doctoral thesis, 2014. http://hdl.handle.net/11858/00-1735-0000-0022-5F7A-6.

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Books on the topic "Tomita algebras"

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Inoue, Atsushi. Tomita-Takesaki theory in algebras of unbounded operators. Berlin: Springer, 1998.

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2

Inoue, Atsushi. Tomita-Takesaki Theory in Algebras of Unbounded Operators. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0093329.

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Inoue, Atsushi. Tomita-Takesaki Theory in Algebras of Unbounded Operators. Springer, 2014.

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Book chapters on the topic "Tomita algebras"

1

Inoue, Atsushi. "Fundamentals of O*-algebras." In Tomita-Takesaki Theory in Algebras of Unbounded Operators, 7–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0093331.

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Antoine, Jean-Pierre, Atsushi Inoue, and Camillo Trapani. "Tomita—Takesaki Theory in Partial O*-Algebras." In Partial *-Algebras and Their Operator Realizations, 165–253. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-017-0065-8_5.

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Inoue, Atsushi. "Standard weights on O*-algebras." In Tomita-Takesaki Theory in Algebras of Unbounded Operators, 111–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0093333.

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4

Inoue, Atsushi. "Introduction." In Tomita-Takesaki Theory in Algebras of Unbounded Operators, 1–5. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0093330.

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Inoue, Atsushi. "Standard systems and modular systems." In Tomita-Takesaki Theory in Algebras of Unbounded Operators, 41–110. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0093332.

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6

Inoue, Atsushi. "Physical applications." In Tomita-Takesaki Theory in Algebras of Unbounded Operators, 169–223. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0093334.

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7

"Tomita-Takesaki Theory." In Introduction to Operator Algebras, 347–68. WORLD SCIENTIFIC, 1992. http://dx.doi.org/10.1142/9789814355865_0008.

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Conference papers on the topic "Tomita algebras"

1

Membreño Estrada, Sharon Samantha, and Claudia Margarita Acuña Soto. "Decision-making problem for interpreting algebraic inequalities / Problemas de toma de decisión para interpretar las inecuaciones algebraicas." In 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. PMENA, 2020. http://dx.doi.org/10.51272/pmena.42.2020-206.

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