The operator algebra approach to quantum groups

DOI10.1073/pnas.97.2.547zbMath0978.46044OpenAlexW2036671267WikidataQ36093937 ScholiaQ36093937MaRDI QIDQ2730673

J. Kustermans, Stefaan Vaes

Publication date: 8 August 2001

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1073/pnas.97.2.547

zbMATH Keywords

duality theorymultiplicative unitarieslocally compact quantum groupKac algebras\(C^*\)-algebra setting

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) (K)-theory and operator algebras (including cyclic theory) (46L80) Quantizations, deformations for selfadjoint operator algebras (46L65)

Related Items (17)

NON-COCOMMUTATIVE C*-BIALGEBRA DEFINED AS THE DIRECT SUM OF FREE GROUP C*-ALGEBRAS ⋮ A quasi-triangular Hopf structure derived from the Burchnall-Chaundy \(C^{\ast}\)-algebra ⋮ Inductive limit violates quasi-cocommutativity ⋮ Triangular \(C^{\ast}\)-bialgebra defined as the direct sum of matrix algebras ⋮ A MEAN ERGODIC THEOREM FOR ACTIONS OF AMENABLE QUANTUM GROUPS ⋮ Operator algebra quantum homogeneous spaces of universal gauge groups ⋮ C\(^*\)-bialgebra defined by the direct sum of Cuntz algebras ⋮ Capacity bounds via operator space methods ⋮ Property (T) and exotic quantum group norms ⋮ The unitary implementation of a locally compact quantum group action ⋮ Pentagon equation arising from state equations of a C\(^*\)-bialgebra ⋮ A REMARK ON QUANTUM GROUP ACTIONS AND NUCLEARITY ⋮ Locally compact quantum groups ⋮ C∗-Bialgebra Defined as the Direct Sum of Cuntz–Krieger Algebras ⋮ Model theory and Rokhlin dimension for compact quantum group actions ⋮ C*-bialgebra Defined as the Direct Sum of UHF Algebras ⋮ Multiresolution analysis for compactly supported interpolating tensor product wavelets

Cites Work

• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Compact matrix pseudogroups
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• An algebraic framework for group duality
• A von Neumann algebra framework for the duality of the quantum groups
• A General Theory of Spectra. I

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