Hopf Algebra Equivariant Cyclic Cohomology, K-theory and Index Formulas
نویسندگان
چکیده
منابع مشابه
Hopf Algebra Equivariant Cyclic Cohomology, K-theory and Index Formulas
For an algebra B with an action of a Hopf algebra H we establish the pairing between 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...
متن کاملHopf Algebra Equivariant Cyclic Cohomology, K-theory and a q-Index Formula
For an algebra B coming with an action of a Hopf algebra H and a twist automorphism, we introduce equivariant twisted cyclic cohomology. In the case when the twist is implemented by a modular element in 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 our cyclic coho...
متن کاملEquivariant Cyclic Cohomology of Hopf Module Algebras
We introduce an equivariant version of cyclic cohomology for Hopf module algebras. For any H-module algebra A, where H is a Hopf algebra with S2 = idH we define the cocyclic module C ♮ H(A) and we find its relation with cyclic cohomology of crossed product algebra A ⋊ H. We define K 0 (A), the equivariant K-theory group of A, and its pairing with cyclic and periodic cyclic cohomology of C H(A).
متن کاملEquivariant Cohomology and Wall Crossing Formulas in Seiberg-Witten Theory
We use localization formulas in the theory of equivariant cohomology to rederive the wall crossing formulas of Li-Liu [7] and Okonek-Teleman [8] for Seiberg-Witten invariants. One of the difficulties in the study of Donaldson invariants or Seiberg-Witten invariants for closed oriented 4-manifold with b2 = 1 is that one has to deal with reducible solutions. There have been a lot of work in this ...
متن کاملBivariant Hopf Cyclic Cohomology
For module algebras and module coalgebras over an arbitrary bialgebra, we define two types of bivariant cyclic cohomology groups called bivariant Hopf cyclic cohomology and bivariant equivariant cyclic cohomology. These groups are defined through an extension of Connes’ cyclic category Λ. We show that, in the case of module coalgebras, bivariant Hopf cyclic cohomology specializes to Hopf cyclic...
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ژورنال
عنوان ژورنال: K-Theory
سال: 2004
ISSN: 1573-0514,0920-3036
DOI: 10.1023/b:kthe.0000031399.40342.7d