A von Neumann algebra framework for the duality of the quantum groups

DOI10.2977/prims/1195165585zbMath0839.46055OpenAlexW2158887514MaRDI QIDQ1890545

Yoshiomi Nakagami, Tetsuya Masuda

Publication date: 12 June 1996

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195165585

zbMATH Keywords

antipodepolar decompositionKac-Takesaki operatorlocally compact quantum groupsleft Hilbert algebrascomultiplicationKac algebraPentagon equationcoassociatvityleft Haar weightWoronowicz algebra

Mathematics Subject Classification ID

Related Items (30)

Extensions of locally compact quantum groups and the bicrossed product construction. ⋮ Characters of infinite-dimensional quantum classical groups: BCD cases ⋮ Actions of multiplier hopf algebras ⋮ LOCALLY COMPACT QUANTUM GROUPS IN THE UNIVERSAL SETTING ⋮ Spherical representations of \(C^\ast\)-flows. II: Representation system and quantum group setup ⋮ Crossed products in bimodules ⋮ The modular automorphism group of a Poisson manifold ⋮ Deformation of a Kac algebra by an abelian subgroup ⋮ Quantum symmetries of the twisted tensor products of \(C^*\)-algebras ⋮ The unitary implementation of a measured quantum groupoid action ⋮ Outer actions of measured quantum groupoids ⋮ From Hopf algebras to topological quantum groups. A short history, various aspects and some problems ⋮ Duality between compactness and discreteness beyond Pontryagin duality ⋮ Amenable tensor categories and their realizations as AFD bimodules ⋮ The operator algebra approach to quantum groups ⋮ The Dirac operator on compact quantum groups ⋮ Inductive limits of compact quantum groups and their unitary representations ⋮ On projective representations for compact quantum groups ⋮ Non-commutative Poisson boundaries and compact quantum group actions ⋮ Inclusions of von Neumann algebras and quantum groupoïds. III ⋮ A quantum \(GL(2,\mathbb{C})\) group at roots of unity ⋮ A REMARK ON QUANTUM GROUP ACTIONS AND NUCLEARITY ⋮ Locally compact quantum groups ⋮ Irreducible inclusions of factors and multiplicative unitaries ⋮ Inclusions of von Neumann algebras, and quantum groupoïds ⋮ An algebraic framework for group duality ⋮ A criterion for a topological group to admit a continuous embedding in a locally compact group ⋮ The canonical endomorphism for infinite index inclusions ⋮ A C*-ALGEBRAIC FRAMEWORK FOR QUANTUM GROUPS ⋮ Inclusions of von Neumann algebras and quantum groupoids. II

Cites Work

• Quantum deformation of Lorentz group
• Zonal spherical functions on the quantum homogeneous space \(\text{SU}_ q(n+1)/\text{SU}_ q(n)\)
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Compact matrix pseudogroups
• Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
• Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups
• Sur la structure des algèbres de Kac. I. (On the structure of Kac algebras. I.)
• Representations of the quantum group \(SU_ q(2)\) and the little q-Jacobi polynomials
• On the Haar measure of the quantum \(SU(N)\) group
• Tomita's theory of modular Hilbert algebras and its applications
• Noncommutative differential geometry on the quantum \(\text{SU}(2)\). I: An algebraic viewpoint
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