Han’s conjecture and its frontiers

In 2006, Yang Han proposed a connection between two homological concepts concerning a finite-dimensional (associative) algebra. In detail, he conjectured that the vanishing (in high degrees) of Hochschild homology of such an algebra implies that its global dimension is finite. Since then, some work has been done in two directions. The first one is concerned in finding examples satisfying the conjecture - which have been seen to include commutative, monomial, Koszul, and group algebras. In a second direction, it has been shown more recently that certain extensions of algebras preserve Han's conjecture. I will present an overview of these works in the seminar's first part. In the second part, I will say roughly how this conjecture behaves in a broader realm of algebras, called pseudocompact algebras. In particular, I will point out that Han's conjecture remains valid in some cases and, for others, that it does not.

All the concepts cited in this abstract will be explained during the presentation.

This is based on my work as a Master's student under the supervision of Kostiantyn Iusenko.