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

Sergey Neshveyev·Lars Tuset
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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.

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Sergey Neshveyev, Lars Tuset. 2003-03-31. Hopf Algebra Equivariant Cyclic Cohomology, K-theory and Index Formulas. https://doi.org/10.1023/b%3Akthe.0000031399.40342.7d

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