Droms’ theorems for twisted right-angled Artin groups.

Abstract: Right-angled Artin groups (RAAGs) form an important link between combinatorics and group theory, since the structure of the group is determined by its defining graph. Twisted right-angled Artin groups (T-RAAGs) generalize this idea by adding directed edges, which allow us to encode both commutation and certain “twisted’’ relations. In this talk, based on joint work with Simone Blumer and Claudio Quadrelli, we explain how Droms’ classical theorems for RAAGs extend to this broader setting. We determine exactly which T-RAAGs have the property that all finitely generated subgroups are again T-RAAGs, give a graph-theoretic criterion for coherence, and solve the isomorphism problem for an important subclass.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.