Algebras determined by $\tau$-slices

TL;DR

This paper introduces a new class of algebras called algebras determined by τ-slices, using τ-tilting theory, and shows they have a bounded representation dimension under certain conditions.

Contribution

It defines algebras determined by τ-slices via τ-tilting theory and establishes an upper bound on their representation dimension.

Findings

Representation dimension of these algebras is at most three.

The concept of τ-slices provides a new perspective on strict laura algebras.

Mild conditions ensure the bounded representation dimension.

Abstract

In this paper we revisit the notion of strict laura algebras through the lens of $\tau$-tilting theory to define the family of algebras determined by $\tau$-slices. We show that the representation dimension of every algebra determined by $\tau$-slices satisfying mild conditions is at most three.