## Séminaire de Géométrie et Quantification |

**Niels
Kowalzig**

(Rome)

When
Ext is a Batalin-Vilkovisky algebra

Lundi
30 janvier
à 15h30, IHP salle **201**,

Résumé : We show under what
conditions the complex computing general Ext-groups

carries the
structure of a cyclic operad such that Ext becomes a

Batalin-Vilkovisky algebra. This is achieved by transferring
cyclic

cohomology theories for the dual of a (left) Hopf
algebroid to the

complex in question, which asks for the notion
of contramodules

introduced along with comodules by
Eilenberg-Moore half a century ago.

Another crucial ingredient
is an explicit formula for the inverse of the

Hopf-Galois map
on the dual, by which we illustrate recent categorical

results
and answer a long-standing open question. As an application, we

prove that the Hochschild cohomology of an associative algebra
A is

Batalin-Vilkovisky if A itself is a contramodule over its
enveloping

algebra A^e. This is, for example, the case for
symmetric algebras and

Frobenius algebras with semisimple
Nakayama automorphism. We also

recover Menichi's construction
for Hopf algebras.

.