Tilting theory, quivers and Auslander – Reiten quivers for everyone

Gabiella D'Este

Università Statale di Milano

I will present some results on Tilting Theory obtained by looking at the underlying abelian groups of rings, modules, bimodules and morphisms. These abelian groups will always be vector spaces over some algebraically closed field K , and their dimension will be countable and almost always finite, as in the classical situation considered by S. Brenner and M.C.R. Butler in “Generalizations of the Bernstein - Gelfand - Ponomarev reflection functors”, Springer LNM 832 (1980). I will show that both discreteand continuous properties show up in a surprising way. Indeed, on the one hand, “simple” and combinatorial objects may have unexpected concealed topological properties. On the other hand, “non simple” objects may have unexpected topological properties.