Actions of compact quantum groups on 𝐶*-algebras

DOI10.1090/S0002-9939-98-04066-0zbMath0885.22009OpenAlexW1506947026MaRDI QIDQ4383035

Marcin Marciniak

Publication date: 24 March 1998

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-98-04066-0

zbMATH Keywords

\(C^*\)-algebrafixed point algebracompact matrix quantum groupTannaka duality theoremtwisted unitary groups

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Applications of selfadjoint operator algebras to physics (46L60)

Related Items (5)

Multiple noncommutative tori as quantum symmetry groups ⋮ Fixed point algebras for easy quantum groups ⋮ Free actions of compact quantum groups on \(C^*\)-algebras. III. ⋮ Fixed points of compact quantum groups actions on Cuntz algebras ⋮ Compact quantum metric spaces and ergodic actions of compact quantum groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new duality theory for compact groups
• Conformal field algebras with quantum symmetry from the theory of superselection sectors
• Derivations vanishing on \(S(\infty)\)
• Some remarks on actions of compact matrix quantum groups on \(C^*\)- algebras
• Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics
• Duals of compact Lie groups realized in the Cuntz algebras and their actions on \(C^ *\)-algebras
• Compact matrix pseudogroups
• Hecke algebras of type \(A_ n\) and subfactors
• Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Extremal traces on some group-invariant C*-algebras
• Simple \(C^*\)-algebras generated by isometries
• Superselection sectors with braid group statistics and exchange algebras
• Free products of compact quantum groups
• Quantum spin chains with quantum group symmetry
• Symmetric states of infinite tensor products of \(C^ *\)-algebras
• Derivations Tangential to Compact Groups: The Non-Abelian Case
• The Crossed Product of a C ∗ -Algebra by an Endomorphism
• Tensor Products and Crossed Products of Compact Quantum Groups
• SUPERSELECTION SECTORS WITH BRAID GROUP STATISTICS AND EXCHANGE ALGEBRAS II: GEOMETRIC ASPECTS AND CONFORMAL COVARIANCE

This page was built for publication: Actions of compact quantum groups on 𝐶*-algebras