Morita Equivalence of Noncommutative Supertori

Details Morita Equivalence of Noncommutative Supertori Morita Equivalence of Noncommutative Supertori

2009-09-30

arxiv.org/abs/0909.5613v4

J.Math.Phys.51:063520,2010

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX 18 pages, the version appeared in JMP

Scientific paper

10.1063/1.3432279

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.

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