Graded Morita equivalence of Clifford superalgebras

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.