The symmetry, period and Calabi-Yau dimension of finite dimensional mesh algebras

TL;DR

This paper classifies finite dimensional mesh algebras based on symmetry and Calabi-Yau properties, providing explicit formulas for their periods and Calabi-Yau dimensions in combinatorial terms.

Contribution

It identifies symmetric and weakly Calabi-Yau mesh algebras and derives explicit combinatorial formulas for their periods and Calabi-Yau dimensions.

Findings

Identification of symmetric mesh algebras

Characterization of weakly Calabi-Yau stable categories

Explicit formulas for periods and Calabi-Yau dimensions

Abstract

Within the class of finite dimensional mesh algebras, also called m-fold mesh algebras, we identify those which are symmetric and those whose stable module category is weakly Calabi-Yau. We also give, in combinatorial terms, explicit formulas for the period of any such algebra, and for the Calabi-Yau Frobenius and stable Calabi-Yau dimensions, when they are defined.