On the Spectrum of Holonomy Algebras

Details On the Spectrum of Holonomy Algebras On the Spectrum of Holonomy Algebras

2002-02-04

arxiv.org/abs/math-ph/0202004v1

J.Geom.Phys. 44 (2002) 96-114

Physics

Mathematical Physics

23 pages, no figures, to appear in J.Geom.Phys

Scientific paper

Connections on a trivial bundle MxG can be identified with their holonomy maps, i.e. with homomorphisms of a groupoid of paths in M into the gauge group G. For a connected compact G, various algebras depending on the set of the smooth connections through their holonomy maps have been introduced in the literature, called cylindrical and holonomy algebras. We discuss the relations between these algebras and the consistence of their spectra.

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