Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2011; 48(3): 505-521

Printed May 1, 2011

https://doi.org/10.4134/BKMS.2011.48.3.505

Copyright © The Korean Mathematical Society.

A remark on Gel'fand duality for spectral triples

Paolo Bertozzini, Roberto Conti, and Wicharn Lewkeeratiyutkul

Thammsat University - Rangsit Campus, University of Newcastle, Chulalongkorn University

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 [5] 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.

Keywords: spectral triple, spin manifold, category

MSC numbers: 46L87, 46M15, 18F99, 15A66

Stats or Metrics

Share this article on :

Related articles in BKMS