Derived tame quadratic string algebras

TL;DR

This paper classifies the derived representation types of quadratic string algebras and shows that derived tame cases with cycles are equivalent to skewed-gentle algebras, advancing understanding of their structure.

Contribution

It provides a complete classification of derived tame quadratic string algebras and establishes their derived equivalence to skewed-gentle algebras when cycles are present.

Findings

Derived tame quadratic string algebras are classified.

Such algebras with cycles are derived equivalent to skewed-gentle algebras.

The paper advances the understanding of the structure and classification of quadratic string algebras.

Abstract

In this paper we determine the derived representation type of quadratic string algebras and we prove that every derived tame quadratic string algebra whose quiver has cycles is derived equivalent to some skewed-gentle algebra.