The conjugacy problem in twisted right-angled Artin groups

Abstract: There exists a vast literature around the idea of constructing groups (and monoids) via some correspondence with finite simple graphs. One well-known example is right-angled Artin groups (RAAGs), where edges in our graph correspond precisely to commuting generators in our group. In this talk, we will discuss an adaptation of this group, known as twisted RAAGs (T-RAAGs), where we introduce the option of ‘Klein-bottle’ relations, which correspond to directed edges of our graph. We will then survey some results about these groups (including many open questions!) and show T-RAAGs have decidable conjugacy problem. This is based on joint work with Islam Foniqi.

Mathematics

Audience: researchers in the topic

ANTLR seminar

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