Morita Equivalence of Noncommutative Supertori

Understand

In this paper we study the extension of Morita equivalence of noncommutative tori to the supersymmetric case.

• The structure of the symmetry group yielding Morita equivalence appears to be intact but its parameter field becomes supersymmetrized having both body and soul parts.
• Our result is mainly in the two dimensional case in which noncommutative supertori have been constructed recently: The group $SO(2,2,V_{\Z}^0)$, where $V_{\Z}^0$ denotes Grassmann even number whose body part belongs to ${\Z}$, yields Morita equivalent noncommutative supertori in two dimensions.