Coactions of Hopf-C-algebras and equivariant E-theory
نویسنده
چکیده
We define and study an equivariant E-theory with respect to coactions of Hopf C-algebras; we prove the Baaj-Skandalis duality in this setting. We show that the corresponding equivariant KK-theory of Baaj and Skandalis enjoys an universal property. In the appendix, we look at the different ways of expressing equivariant stability for a functor, and prove an equivariant BrownGreen-Rieffel stabilization result. MSC 2000: primary 46L80, secondary 19K56, 22D25
منابع مشابه
Duality for Actions
Let G be a locally compact group. We show that the category A(G) of actions of G on C∗-algebras (with equivariant nondegenerate ∗-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C∗(G), δG); and also that A(G) is equivalent, via a reduced-crossed-product functor, to a comma catego...
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 کاملCyclic Cohomology of Hopf Module Algebras
We define an equivariant K0-theory for Yetter-Drinfeld algebras over a Hopf algebra with an invertible antipode. We show that there exists a pairing, generalizing Connes’ pairing, between this theory and a suitably defined Hopf algebra equivariant cyclic cohomology theory.
متن کاملA New Cyclic Module for Hopf Algebras
We define a new cyclic module, dual to the Connes-Moscovici cyclic module, for Hopf algebras, and give a characteristric map for coactions of Hopf algebras. We also compute the resulting cyclic homology for cocommutative Hopf algebras, and some quantum groups.
متن کاملEquivariant Spectral Triples
We present the review of noncommutative symmetries applied to Connes’ formulation of spectral triples. We introduce the notion of equivariant spectral triples with Hopf algebras as isometries of noncommutative manifolds, relate it to other elements of theory (equivariant K-theory, homology, equivariant differential algebras) and provide several examples of spectral triples with their isometries...
متن کامل