The number of two-term tilting complexes over symmetric algebras with radical cube zero

TL;DR

This paper classifies symmetric algebras with radical cube zero that have finitely many two-term tilting complexes and provides explicit counts for each case, advancing understanding of their derived categories.

Contribution

It offers a complete classification and enumeration of two-term tilting complexes over symmetric algebras with radical cube zero, a previously uncharted area.

Findings

Identified symmetric algebras with finite two-term tilting complexes

Provided explicit counts for each algebra case

Connected algebraic structures to their associated graphs

Abstract

In this paper, we compute the number of two-term tilting complexes for an arbitrary symmetric algebra with radical cube zero over an algebraically closed field. Firstly, we give a complete list of symmetric algebras with radical cube zero having only finitely many isomorphism classes of two-term tilting complexes in terms of their associated graphs. Secondly, we enumerate the number of two-term tilting complexes for each case in the list.