On the cyclic Homology of multiplier Hopf algebras

NOTES ON REGULAR MULTIPLIER HOPF ALGEBRAS

In this paper, we associate canonically a precyclic mod- ule to a regular multiplier Hopf algebra endowed with a group-like projection and a modular pair in involution satisfying certain con- dition

Cyclic Homology of Hopf Comodule Algebras and Hopf Module Coalgebras

In this paper we construct a cylindrical module A♮H for an Hcomodule algebra A, where the antipode of the Hopf algebra H is bijective. We show that the cyclic module associated to the diagonal of A♮H is isomorphic with the cyclic module of the crossed product algebra A ⋊H. This enables us to derive a spectral sequence for the cyclic homology of the crossed product algebra. We also construct a c...

notes on regular multiplier hopf algebras

in this paper, we associate canonically a precyclic mod- ule to a regular multiplier hopf algebra endowed with a group-like projection and a modular pair in involution satisfying certain con- dition

Hopf Algebra Equivariant Cyclic Homology and Cyclic Homology of Crossed Product Algebras

We introduce the cylindrical module A♮H, where H is a Hopf algebra with S2 = idH and A is a Hopf module algebra over H. We show that there exists a cyclic map between the cyclic module of the crossed product algebra A⋊H and ∆(A♮H), the cyclic module related to the diagonal of A♮H. In the cocommutative case, ∆(A♮H) ∼= C•(A ⋊H). Finally we approximate ∆(A♮H) by a spectral sequence and we give an ...

On the Coderivations of Some Hopf Algebras

Homology TQFT’s via Hopf Algebras

In [5] Frohman and Nicas define a topological quantum field theory via the intersection homology of U(1)-representation varieties J(X) = Hom(π1(X), U(1)). We show that this TQFT is equivalent to the combinatorially constructed Hennings-TQFT based on the quasitriangular Hopf algebra N = Z/2 ⋉ ∧ ∗ R. The natural SL(2,R)-action on N is identified with the SL(2,R)action for the Lefschetz decomposit...