Cohomological symmetry in triangulated categories

TL;DR

This paper establishes a criterion for cohomological symmetry in triangulated categories and demonstrates its validity for all module pairs over exterior algebras, advancing understanding in algebraic structures.

Contribution

It introduces a new criterion for cohomological symmetry and applies it to modules over exterior algebras, showing broad applicability.

Findings

Cohomological symmetry criterion provided

Symmetry holds for modules over exterior algebras

Advances understanding of algebraic cohomological properties

Abstract

We give a criterion for cohomological symmetry in a triangulated category. As an application, we show that such cohomological symmetry holds for all pairs of modules over any exterior algebra.