Morita "equivalences" of equivariant torus spectral triples

TL;DR

This paper demonstrates that Morita equivalence becomes an equivalence relation specifically for equivariant torus spectral triples, clarifying the conditions under which this relation is symmetric.

Contribution

It establishes that Morita equivalence is symmetric for equivariant torus spectral triples, resolving a non-symmetry issue in the general case.

Findings

Morita equivalence is an equivalence relation for equivariant torus spectral triples

Symmetry of Morita equivalence holds in this specific setting

Clarifies the structure of spectral triples under Morita equivalence

Abstract

In general, Morita equivalence of spectral triples need not be a symmetric relation. In this paper, we show that Morita equivalence of spectral triples is an equivalence relation for equivariant torus spectral triples.