Stable Calabi--Yau dimension of self-injective algebras of finite type

TL;DR

This paper provides an equivalent definition of the stable Calabi--Yau dimension for self-injective algebras and completes the calculation of these dimensions for all finite type cases, advancing understanding in algebraic representation theory.

Contribution

It introduces a new definition of stable Calabi--Yau dimension and completes the classification for finite type self-injective algebras.

Findings

Complete computation of stable Calabi--Yau dimensions for finite type algebras

New characterization using bimodule syzygies and stably inner automorphisms

Clarification of the structure of self-injective algebras of finite type

Abstract

We give an equivalent definition of the stable Calabi--Yau dimension in terms of bimodule syzygies and so-called stably inner automorphisms. Using it, we complete the computation of the stable Calabi--Yau dimensions of the self-injective algebras of finite representation type which was started by K. Erdmann, A. Skowro\'nski, J. Bia\lkowski and A. Dugas.