Tuesday, October 8, 14:00, 7.527.

Lleonard Rubio y Degrassi
On the first relative Hochschild cohomology and contracted fundamental group I, II.

Abstract:
In 1956 Hochschild introduced the notion of relative Hochschild cohomology. Recently, relative Hochschild cohomology has been used by Cibils, Lanzilotta, Marcos, Schroll and Solotar to describe how the Hochschild cohomology of a bound quiver algebra changes when adding or deleting arrows from the quiver.

Let A be a bound quiver algebra and let B be a subalgebra of A having the same semisimple part. In this talk, I will give a sufficient condition for the solvability of the first relative Hochschild cohomology HH¹(A|B). I will also introduce a relative version of the fundamental group of a bound quiver. Similarly to the classical case, I will show how these groups are related to the first relative Hochschild cohomology.

This talk is based on joint work with Jonathan Lindell.