A remark on Gel'fand duality for spectral triples
Bull. Korean Math. Soc. 2011 Vol. 48, No. 3, 505-521
https://doi.org/10.4134/BKMS.2011.48.3.505
Published online May 1, 2011
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
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