### Research group:

New Results in Hopf-cyclic Cohomology

#### 21 – 24 May, 2011, Warsaw

### Organizer

P.M. Hajac

### Programme

**Monday, 23rd of May**

10.15, room 322

**CYCLIC STRUCTURES IN ALGEBRAIC (CO)HOMOLOGY THEORIES **

The cyclic cohomology of a left Hopf algebroid with coefficients in a right module left comodule is defined using a straightforward generalisation of the original operators given by Connes and Moscovici for Hopf algebras. A form of cyclic duality that makes sense for arbitrary para-cyclic objects yields a dual homology theory. The twisted cyclic homology of an associative algebra provides an example of this dual theory that uses coefficients that are not necessarily stable anti-Yetter-Drinfeld modules. (Joint work with N. Kowalzig.)

**ULRICH KRAEHMER (University of Glasgow, Scotland)**

**Monday, 23rd of May 2011**

14.15, room 322

**CUP PRODUCTS IN HOPF-CYCLIC COHOMOLOGY WITH COEFFICIENTS IN CONTRAMODULES **

We use stable anti-Yetter-Drinfeld contramodules as coefficients of Hopf-cyclic cohomology to achieve the functoriality of cup products. This generalization of original cup products in Hopf-cyclic cohomology allows us to define them for two different stable anti-Yetter-Drinfeld modules. To show that the choice of coefficients is important, we prove the non-trivial dependence of cup products on coefficients.

**BAHRAM RANGIPOUR (University of New Brunswick, Fredericton, Canada)**

### Participants

- P.M. Hajac (IM PAN, Warsaw, Poland)
- U. Kraehmer (Glasgow, Scotland)
- T. Maszczyk (Warsaw, Poland)
- B. Rangipour (Fredericton, Canada)