Galois groups of quantum group actions and regularity of fixed-point algebras

DOI10.1090/S0002-9947-03-03282-3zbMath1034.46069MaRDI QIDQ4806460

Takehiko Yamanouchi

Publication date: 14 May 2003

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

regularityfactoractionlocally compact quantum group

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) General theory of von Neumann algebras (46L10) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Quantizations, deformations for selfadjoint operator algebras (46L65)

Cites Work

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• Extension of Jones' theory on index of arbitrary factors
• A Galois correspondence for compact groups of automorphisms of von Neumann algebras with a generalization to Kac algebras
• The Connes spectrum for actions of compact Kac algebras and factoriality of their crossed products
• Lattices of intermediate subfactors for type III factors
• Description of the automorphism group \(\text{Aut}({\mathcal A}/{\mathcal A}^\alpha)\) for a minimal action of a compact Kac algebra and its application
• Vecteurs totalisateurs d'une algébre de von Neumann
• The structure of a von Neumann algebra with a homogeneous periodic state
• Entropy and index for subfactors
• On the Intrinsic Group of a Kac Algebra
• Locally compact quantum groups in the von Neumann algebraic setting
• On the dominancy of minimal actions of compact Kac algebras and certain automorphisms in $\mathrm{Aut}(A/A^\alpha)$
• Locally compact quantum groups
• The unitary implementation of a locally compact quantum group action
• Uniqueness of Haar measures for a quasi Woronowicz algebra

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