### Séminaire Topologies

Le jeudi 14 septembre 2017 à 10:10 - salle 430

Spécial
Deux exposés d'algèbre non commutative (Eduardo do Nascimento Marcos et Andrea Solotar)

10:10-11:00
Eduardo do Nascimento Marcos (Universidade de Sao Paulo, Brazil)
Hochschild cohomology of a smash product in the nonsemisimple case

This will be a talk on a joint work with Yury Volkov. We explore the relations between the Hochschild cohomology of an algebra over some field and the Hochschild cohomology of its smash product with a finite group. Basically we are concentrated on the case where the group under consideration is an extension of a cyclic $p$-group by some $p'$-group, where $p$ is the characteristic of the ground field.

11:20-12:10
Andrea Solotar (Universidad de Buenos Aires, Argentina)
Homological invariants relating the super Jordan plane to the Virasoro algebra

This will be a talk on a joint work with Sebastian Reca. We study homological invariants of the super Jordan plane, that is, the Nichols algebra A = B(V(-1, 2)). These invariants are Hochschild homology, the Hochschild cohomology algebra, the Lie structure of the first cohomology space - which is a Lie subalgebra of the Virasoro algebra - and its representations H^n(A, A) and also the Yoneda algebra. Moreover, we prove that the Yoneda algebra of its bosonization A#kZ is finitely generated.

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