Calabi-Yau properties of ribbon graph orders

TL;DR

This paper investigates the Calabi-Yau properties of ribbon graph orders, showing they are twisted 1-Calabi-Yau generally and 1-Calabi-Yau for bipartite graphs, with applications to Brauer graph algebras.

Contribution

It establishes the Calabi-Yau properties of ribbon graph orders and their anti-commutative variants, extending the order-theoretic approach to these structures.

Findings

Ribbon graph orders are twisted 1-Calabi-Yau.

Bipartite ribbon graphs yield 1-Calabi-Yau orders.

Results apply to anti-commutative Brauer graph algebras.

Abstract

We pursue the order-theoretic approach to ribbon graphs initiated by Kauer and Roggenkamp. We show that any ribbon graph order is twisted $1$-Calabi-Yau in general and $1$-Calabi-Yau if the ribbon graph is bipartite. We derive analogous results for anti-commutative versions of Brauer graph algebras.