Stability conditions, $\tau$-tilting Theory and Maximal Green Sequences

Abstract

Extending the notion of maximal green sequences to an abelian category, we characterize the stability functions, as defined by Rudakov, that induce a maximal green sequence in an abelian length category. Furthermore, we use $\tau$-tilting theory to give a description of the wall and chamber structure of any finite dimensional algebra. Finally we introduce the notion of green paths in the wall and chamber structure of an algebra and show that green paths serve as geometrical generalization of maximal green sequences in this context.

Cited by in corpus (11)

• Wall and Chamber Structure for finite-dimensional Algebras
• Silting objects
• Wide subcategories are semistable
• A survey on maximal green sequences
• Linearity of stability conditions
• Maximal green sequences for cluster-tilted algebras of finite representation type
• Stability conditions for affine type A
• Higher support tilting I: higher Auslander algebras of linearly oriented type $A$
• Maximal green sequences of quivers with multiple edges
• Horizontal and vertical mutation fans
• Cluster algebras and their bases