Hopf Algebra Equivariant Cyclic Cohomology, K-theory and Index Formulas

Abstract

For an algebra B with an action of a Hopf algebra H we establish the pairing between even equivariant cyclic cohomology and equivariant K-theory for B. We then extend this formalism to compact quantum group actions and show that equivariant cyclic cohomology is a target space for the equivariant Chern character of equivariant summable Fredholm modules. We prove an analogue of Julg's theorem relating equivariant K-theory to ordinary K-theory of the C*-algebra crossed product, and characterize equivariant vector bundles on quantum homogeneous spaces.

LaTeX2e, 16 pages; corrections plus a short discussion of K1

Cited by in corpus (15)

• A Local Index Formula for the Quantum Sphere
• Anti-selfdual Connections on the Quantum Projective Plane: Monopoles
• Equivariant Poincaré duality for quantum group actions
• On the noncommutative spin geometry of the standard Podles sphere and index computations
• Modular Invariants and Twisted Equivariant K-theory
• Twisted Cyclic Cohomology and Modular Fredholm Modules
• Equivariant cyclic homology for quantum groups
• Geometry of the quantum projective plane
• The universal Hopf cyclic theory
• Dirac Operators on Quantum Weighted Projective Spaces
• Twisted homology of quantum SL(2)
• Quantum Bianchi identities and characteristic classes via DG categories
• Constant and Equivariant Cyclic Cohomology
• Twisted Hochschild homology of quantum flag manifolds: 2-cycles from invariant projections
• Hopf--Hochschild (co)homology of module algebras