A Remark on Gelfand Duality for Spectral Triples
Operator Algebras
2011-12-30 v2 Category Theory
Abstract
We present a duality between the category of compact Riemannian spin manifolds (equipped with a given spin bundle and charge conjugation) with isometries as morphisms and a suitable "metric" category of spectral triples over commutative pre-C*-algebras. We also construct an embedding of a "quotient" of the category of spectral triples introduced in arXiv:math/0502583v1 into the latter metric category. Finally we discuss a further related duality in the case of orientation and spin-preserving maps between manifolds of fixed dimension.
Cite
@article{arxiv.0812.3584,
title = {A Remark on Gelfand Duality for Spectral Triples},
author = {Paolo Bertozzini and Roberto Conti and Wicharn Lewkeeratiyutkul},
journal= {arXiv preprint arXiv:0812.3584},
year = {2011}
}
Comments
15 pages, AMS-LaTeX2e, results unchanged, several improvements in the exposition, appendix added