Date(s) - 02/02/2023 10:30 am - 11:30 am
Abstract: Tiled orders are a class of orders in central simple algebras generalizing maximal, hereditary, and Eichler orders. Also known as graduated or split orders, they have arisen in various contexts of representation theory and algebra, and exhibit surprising combinatorial properties. For example, Shemanske showed in 2010 that one could associate to each tiled order a convex polytope in a building, and in 2002 Haefner and Pappacena interpreted some of their properties via an associated quiver (i.e. a multidigraph). In this talk, I will focus on the latter interpretation, and examine the normalizer of a tiled order via automorphisms of valued directed graphs.