The Representation Dimension of a Selfinjective Algebra of Wild Tilted Type

TL;DR

This paper proves that selfinjective algebras of wild tilted type have a representation dimension of three and provides an explicit Auslander generator, advancing understanding of their module categories.

Contribution

It establishes the exact representation dimension for a class of selfinjective algebras and constructs explicit Auslander generators, extending prior theoretical results.

Findings

Representation dimension of wild tilted selfinjective algebras is three.

Explicit construction of an Auslander generator for these algebras.

Connected selfinjective algebras with certain Auslander-Reiten components also have representation dimension three.

Abstract

We prove that the representation dimension of a selfinjective algebra of wild tilted type is equal to three, and give an explicit construction of an Auslander generator of its module category. We also show that if a connected selfinjective algebra admits an acyclic generalised standard Auslander-Reiten component then its representation dimension is equal to three.