DISCRETE NON-COMMUTATIVE GEL’FAND-NA˘IMARK DUALITY

  • Paolo Bertozzin
  • Roberto Conti
  • Natee Pitiwan
Keywords: C*-algebra, C*-category, Fell Bundle, Spectrum, Duality, Non-commutative Topology

Abstract

We present, in a simplified setting, a non-commutative version of the wellknown Gel’fand-Na˘ımark duality (between the categories of compact Hausdorff topological spaces and commutative unital C*-algebras), where “geometric spectra” consist of suitable finite bundles of one-dimensional C*-categories equipped with a transition amplitude structure satisfying saturation conditions. Although thisdiscretedualityactuallydescribesthetrivialcaseoffinite-dimensionalC*-algebras, the structures are here developed at a level of generality adequate for the formulation of a general topological/uniform Gel’fand-Na˘ımark duality, fully addressed in a companion work.

Published
2020-02-04