Derived Hall algebras of one-cycle gentle algebras: The infinite global dimension case

TL;DR

This paper characterizes the derived Hall algebras of one-cycle gentle algebras with infinite global dimension using generators and relations, advancing understanding of their algebraic structure.

Contribution

It provides a detailed presentation of the derived Hall algebras for a specific class of gentle algebras with infinite global dimension, which was previously unexplored.

Findings

Explicit generators and relations for the derived Hall algebras derived.

Identification of algebraic structures specific to infinite global dimension case.

Enhanced understanding of the algebraic properties of one-cycle gentle algebras.

Abstract

We describe, in terms of generators and relations, the derived Hall algebras associated to the one-cycle gentle algebras of infinite global dimension.