Support varieties - an axiomatic approach

TL;DR

This paper introduces an axiomatic framework for analyzing support varieties within triangulated categories influenced by tensor actions, extending to non-symmetric tensor contexts, with applications in finite-dimensional algebra representations.

Contribution

It develops a new axiomatic approach to support varieties in triangulated categories with tensor actions, including non-symmetric cases, and demonstrates applications in representation theory.

Findings

Axiomatic framework for support varieties in triangulated categories

Extension to non-symmetric tensor actions

Applications to finite-dimensional algebra representations

Abstract

We provide an axiomatic approach for studying support varieties of objects in a triangulated category via the action of a tensor triangulated category, where the tensor product is not necessarily symmetric. This is illustrated by examples, taken in particular from representation theory of finite dimensional algebras.