Licentiate Seminar: On the First Relative Hochschild Cohomology and Contracted Fundamental Group

Supervisor is Julian Külshammer and the external reviewer is Professor Emeritus Claude Cibils at Université de Montpellier.

Abstract: In this paper we investigate the Lie algebra structure of the first relative Hochschild cohomology and its relation with the relative notion of fundamental group. Let A, B be finite-dimensional basic k-algebras over an algebraically closed field of characteristic zero, such that QB is a subquiver of QA. We show that if the complement of QA by the arrows of QB is a simple directed graph, then the first relative Hochschild cohomology HH1(A|B) is a solvable Lie algebra. We also compute the Lie algebra structure of the first relative Hochschild cohomology for radical square zero algebras and for dual extension algebras of directed monomial algebras. Finally, we introduce the notion of fundamental group for a pair of an algebra A and a subalgebra B and we construct the relative version of the map from the dual fundamental group into the first Hochschild cohomology.

A link to the thesis in DiVA will appear in this list as soon as it is published there.