Algebraic properties of zigzag algebras

TL;DR

This paper investigates the algebraic structures of zigzag algebras, establishing conditions under which they possess properties like cellularity, quasi-heredity, or Koszulity, thus advancing understanding of their theoretical framework.

Contribution

It provides necessary and sufficient criteria for zigzag algebras to be cellular, quasi-hereditary, or Koszul, expanding the theoretical knowledge of these algebraic structures.

Findings

Criteria for zigzag algebras to be cellular

Conditions for quasi-heredity in zigzag algebras

When zigzag algebras are Koszul

Abstract

We give necessary and sufficient conditions for zigzag algebras and certain generalizations of them to be (relative) cellular, quasi-hereditary or Koszul.