TY - JOUR
T1 - Induced c* -algebras and landstad duality for twisted coactions
AU - Quigg, John
AU - Raeburn, Iain
N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
PY - 1995/8
Y1 - 1995/8
N2 - Suppose N is a closed normal subgroup of a locally compact group G. A coaction e: A → M(A and C*(N)) of N on a C*-algebra A can be inflated to a coaction S of G on A, and the crossed product A × δ G is then isomorphic to the induced C*-algebra IndGNA× ε N. We prove this and a natural generalization in which A × ε N is replaced by a twisted crossed product A × G/NG; in case G is abelian, we recover a theorem of Olesen and Pedersen. We then use this to extend the Landstad duality of the first author to twisted crossed products, and give several applications. In particular, we prove that if 1 → N → G → G/N → 1 is topologically trivial, but not necessarily split as a group extension, then every twisted crossed product A × G/NG is isomorphic to a crossed product of the form A x N.
AB - Suppose N is a closed normal subgroup of a locally compact group G. A coaction e: A → M(A and C*(N)) of N on a C*-algebra A can be inflated to a coaction S of G on A, and the crossed product A × δ G is then isomorphic to the induced C*-algebra IndGNA× ε N. We prove this and a natural generalization in which A × ε N is replaced by a twisted crossed product A × G/NG; in case G is abelian, we recover a theorem of Olesen and Pedersen. We then use this to extend the Landstad duality of the first author to twisted crossed products, and give several applications. In particular, we prove that if 1 → N → G → G/N → 1 is topologically trivial, but not necessarily split as a group extension, then every twisted crossed product A × G/NG is isomorphic to a crossed product of the form A x N.
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U2 - 10.1090/S0002-9947-1995-1297536-3
DO - 10.1090/S0002-9947-1995-1297536-3
M3 - Article
AN - SCOPUS:0007056120
SN - 0002-9947
VL - 347
SP - 2885
EP - 2915
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 8
ER -