Naturality and Induced Representations

Details Naturality and Induced Representations Naturality and Induced Representations

2000-02-04

arxiv.org/abs/math/0002039v1

Mathematics

Operator Algebras

LaTeX-2e, 24 pages, uses package pb-diagram

Scientific paper

We show that induction of covariant representations for C*-dynamical systems is natural in the sense that it gives a natural transformation between certain crossed-product functors. This involves setting up suitable categories of C*-algebras and dynamical systems, and extending the usual constructions of crossed products to define the appropriate functors. From this point of view, Green's Imprimitivity Theorem identifies the functors for which induction is a natural equivalence. Various spcecial cases of these results have previously been obtained on an ad hoc basis.

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