Graded Morita equivalence of Clifford superalgebras

TL;DR

This paper explicitly classifies graded basic superalgebras for all real and complex Clifford superalgebras using a variation of graded Morita theory, and describes their Grothendieck groups of graded modules.

Contribution

It provides an explicit classification of graded basic superalgebras for Clifford superalgebras and computes their Grothendieck groups, advancing understanding of their module categories.

Findings

Explicit graded basic superalgebras for all Clifford superalgebras determined.

Grothendieck groups of graded modules over Clifford superalgebras described.

Application of graded Morita theory to superalgebras demonstrated.

Abstract

This note uses a variation of graded Morita theory for finite dimensional superalgebras to determine explicitly the graded basic superalgebras for all real and complex Clifford superalgebras. As an application, the Grothendieck groups of the category of left $\mathbb{Z}_2$-graded modules over all real and complex Clifford superalgebras are described explicitly.