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

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

2003-03-31

arxiv.org/abs/math/0304001v3

Mathematics

K-Theory and Homology

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

Scientific paper

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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