TY - JOUR
T1 - Naturality and induced representations
AU - Echterhoff, Siegfried
AU - Kaliszewski, Steven
AU - Quigg, John
AU - Raeburn, Iain
PY - 2000/6
Y1 - 2000/6
N2 - 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 special cases of these results have previously been obtained on an ad hoc basis.
AB - 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 special cases of these results have previously been obtained on an ad hoc basis.
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U2 - 10.1017/S0004972700022449
DO - 10.1017/S0004972700022449
M3 - Article
AN - SCOPUS:0034196266
SN - 0004-9727
VL - 61
SP - 415
EP - 438
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 3
ER -