Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Geometry and Representation Theory Seminar


Monday, December 3rd, 2018

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 319

Speaker: Kaveh Mousavand (UQAM)

Title: $\tau$-tilting finiteness of special biserial algebras

Abstract:  $\tau$-tilting theory, recently introduced by Adachi-Iyama-Reiten, is an elegant generalization of the classical tilting theory which fixes the deficiency of the tilting modules with respect to the notion of mutation. In this talk, I view $\tau$-tilting finiteness of algebras as a natural generalization of the representation finiteness property. The natural question then becomes: For which families of algebras does $\tau$-tilting finiteness imply representation finiteness?

First I introduce a reductive method that can be applied to certain families of algebras to reduce this, a priori, intractable problem to a subfamily with nice features. Then, as an interesting class of algebras, I consider the special biserial algebras and for every minimal representation infinite member of this family, I give a full answer to the above question and show. As a corollary, we conclude that a gentle algebra is $\tau$-tilting finite if and only if it is representation finite.