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 -