Minimal ($\tau$)-tilting Infinite Algebras

Abstract: Motivated by a new conjecture on $\tau$-tilting infinite algebras, we study minimal $\tau$-tilting infinite algebras as a modern counterpart of minimal representation infinite algebras. This talk begins by a discussion of some fundamental similarities and differences between these two families of algebras. Then we relate our studies to the classical tilting theory. In particular, for each minimal $\tau$-tilting infinite algebra $A$, we show that the mutation graph of tilting $A$-modules is infinite and almost $n$-regular at each vertex, where $n$ is the rank of Grothendieck group of $A$.

This is a report on my joint work with Charles Paquette.

combinatoricscategory theoryrepresentation theory

Audience: researchers in the topic

( slides )

The TRAC Seminar - Théorie de Représentations et ses Applications et Connections