Gauge-equivariant Hilbert bimodules and crossed products by endomorphisms

Details Gauge-equivariant Hilbert bimodules and crossed products by endomorphisms Gauge-equivariant Hilbert bimodules and crossed products by endomorphisms

2007-05-21

arxiv.org/abs/0705.2933v5

International Journal of Mathematics 20(11) (2009) 1363-1396

Mathematics

Operator Algebras

28 pages; corrected an error in Ex.6.3.2 of the previous version

Scientific paper

C*-endomorphisms arising from superselection structures with non-trivial centre define a 'rank' and a 'first Chern class'. Crossed products by such endomorphisms involve the Cuntz-Pimsner algebra of a vector bundle having the above-mentioned rank and first Chern class, and can be used to construct a duality for abstract (nonsymmetric) tensor categories vs. group bundles acting on (nonsymmetric) Hilbert bimodules. Existence and unicity of the dual object (i.e., the 'gauge' group bundle) are not ensured: we give a description of this phenomenon in terms of a certain moduli space associated with the given endomorphism. The above-mentioned Hilbert bimodules are noncommutative analogues of gauge-equivariant vector bundles in the sense of Nistor-Troitsky.

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