Morita Equivalence of Noncommutative Supertori

TL;DR

This paper extends Morita equivalence concepts from noncommutative tori to noncommutative supertori, revealing that the symmetry group structure remains similar but with supersymmetrized parameters, especially in two dimensions.

Contribution

It introduces the supersymmetrized Morita equivalence framework for noncommutative supertori, focusing on the two-dimensional case with a specific symmetry group.

Findings

The symmetry group for Morita equivalence is preserved in the supersymmetric extension.

In two dimensions, the group SO(2,2,V_Z^0) yields Morita equivalent noncommutative supertori.

The parameter field becomes supersymmetrized, incorporating both body and soul parts.

Abstract

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.