Strongly Periodic Modules and Perverse Autoequivalences

TL;DR

This paper introduces the concept of strong periodicity in modules over finite-dimensional algebras and links it to two-step self-perverse equivalences, with applications to symmetric groups.

Contribution

It establishes a new criterion connecting strong periodicity of modules to the existence of specific autoequivalences in algebra.

Findings

Strong periodicity characterizes certain autoequivalences.

Necessary and sufficient conditions for two-step self-perverse equivalences.

Applications demonstrated in the context of symmetric groups.

Abstract

We introduce a notion of strong periodicity of a module over a finite-dimensional algebra over a field. We prove that the existence of such modules over certain idempotent algebras is both a necessary and sufficient condition for the existence of a two-step self-perverse equivalence of a finite-dimensional algebra. We survey some applications to the setting of the symmetric groups.