Invariance of representation dimension under socle equivalence of selfinjective algebras

TL;DR

This paper proves that the representation dimension of finite dimensional selfinjective algebras remains unchanged under socle equivalence, providing insights into their structural invariants.

Contribution

It establishes the invariance of representation dimension under socle equivalence for selfinjective algebras, a new result in algebra representation theory.

Findings

Representation dimension is invariant under socle equivalence.

Derived consequences for algebra classification.

Enhanced understanding of algebra invariants.

Abstract

We prove that the representation dimension of finite dimensional selfinjective algebras over a field is invariant under socle equivalence and derive some consequences.