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.



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