Induced c* -algebras and landstad duality for twisted coactions

John Quigg, Iain Raeburn

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)2885-2915
Number of pages31
JournalTransactions of the American Mathematical Society
Volume347
Issue number8
DOIs
StatePublished - Aug 1995

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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