Classifying τ-tilting modules over preprojective algebras of Dynkin type

Abstract

We study support $\tau$-tilting modules over preprojective algebras of Dynkin type. We classify basic support $\tau$-tilting modules by giving a bijection with elements in the corresponding Weyl groups. Moreover we show that they are in bijection with the set of torsion classes, the set of torsion-free classes and other important objects in representation theory. We also study $g$-matrices of support $\tau$-tilting modules, which show terms of minimal projective presentations of indecomposable direct summands. We give an explicit description of $g$-matrices and prove that cones given by $g$-matrices coincide with chambers of the associated root systems.

26 pages. Minor changes, to appear in Math. Z

References in corpus (1)

• Affine Mirković-Vilonen polytopes

Cited by in corpus (2)

• Stability conditions and quantum dilogarithm identities for Dynkin quivers
• Characterizing τ-rigid-finite algebras with radical square zero