# Claude Cibils: Han's conjecture and split extension algebras

**Time: **
Wed 2019-06-05 13.15 - 14.15

**Location: **
Room 3418, KTH

**Participating: **
Claude Cibils (Montpellier)

Abstract: Hochschild homology is a powerful tool, which is closely related with cyclic homology through the Connes-Tsygan periodicity sequence. Han's conjecture states that if the Hochschild homology of a finite dimensional associative algebra A stops, then A is "smooth" in the sense that it has finite global dimension. For commutative algebras this has been proved by L. Avramov and M. Vigué-Poirrier, and by the "Buenos Aires Cyclic Homology Group" in the 90's.

We will recall Hochschild homology, its relative version, and a Jacobi-Zariski long exact sequence relating them, obtained recently by A. Kaygun. Then we will consider under what conditions the class of algebras satisfying Han's conjecture is closed under split extensions, as a step towards proving the conjecture. Algebras presented by quivers and relations are concerned, through adding arrows.

This is a joint work with M. Lanzilotta, E. Marcos and A. Solotar.