Perverse equivalences, BB-tilting, mutations and applications

TL;DR

This paper explores the relationships between BB-tilting, perverse derived equivalences, and mutations of algebras, providing new tools for understanding derived equivalences and their applications in cluster-tilting theory.

Contribution

It introduces a framework connecting BB-tilting and perverse equivalences, defining algebra mutations that preserve derived equivalence, with applications to specific algebra classes.

Findings

Established a link between BB-tilting and perverse equivalences.

Defined algebra mutations that preserve derived equivalence.

Applied results to cluster-tilting objects and low global dimension algebras.

Abstract

We relate the notions of BB-tilting and perverse derived equivalence at a vertex. Based on these notions, we define mutations of algebras, leading to derived equivalent ones. We present applications to endomorphism algebras of cluster-tilting objects in 2-Calabi-Yau categories and to algebras of global dimension at most 2.