Codes and Expansions (CodEx) Seminar

Assaf Goldberger (Tel Aviv University):
Switching Automorphisms and centralizer algebras with commutative and non-commutative coefficients, a cohomological point of view

Switching automorphisms of point and line configurations are an active field of study. The most common approach identifies the gram matrix of a configuration as a centralizing element of a certain monomial projective representation of the switching automorphism group. In this talk we will offer a different point of view, of cohomolgy of groups. The tools that we shall employ are taken from homological algebra. This explains the appearance of cohomlogy in the projective representation, as well as other related concepts such as two-graphs. It also carries a topological interpretation and can be widely generalized to broader contexts. Time permitting, we will discuss how to work with non-commutative coefficients coming from a nilpotent group, the quaternion group being an example.