Wall and Chamber Structure for finite-dimensional Algebras

TL;DR

This paper employs $ au$-tilting theory to describe the wall and chamber structure of finite-dimensional algebras and links maximal green sequences to $rak{D}$-generic paths, advancing understanding of algebraic mutation processes.

Contribution

It introduces a novel description of wall and chamber structures using $ au$-tilting theory and connects maximal green sequences with $rak{D}$-generic paths in these structures.

Findings

Wall and chamber structures characterized via $ au$-tilting theory

Maximal green sequences are induced by $rak{D}$-generic paths

Provides new insights into algebraic mutation processes

Abstract

We use $\tau$-tilting theory to give a description of the wall and chamber structure of a finite dimensional algebra. We also study $\mathfrak{D}$-generic paths in the wall and chamber structure of an algebra $A$ and show that every maximal green sequence in mod $A$ is induced by a $\mathfrak{D}$-generic path.