Crossed products by semigroups of endomorphisms and the toeplitz algebras of ordered groups

Sriwulan Adji, Marcelo Laca, May Nilsen, Iain Raeburn

Research output: Contribution to journalArticle

62 Scopus citations

Abstract

Let ℸ+ be the positive cone in a totally ordered abelian group ℸ. We construct crossed products by actions of ℸ+ as endomorphisms of Calgebras, and give criteria which ensure a given representation of the crossed product is faithful. We use this to prove that the C* -algebras generated by two semigroups V, W: ℸ+ → B (H) of nonunitary isometries are canonically isomorphic, thus giving a new, self-contained proof of a theorem of Murphy, which includes earlier results of Coburn and Douglas.

Original languageEnglish (US)
Pages (from-to)1133-1141
Number of pages9
JournalProceedings of the American Mathematical Society
Volume122
Issue number4
DOIs
StatePublished - Dec 1994

Keywords

  • C*-algebra
  • Covariant representation
  • Crossed product
  • Endomorphism
  • Ordered group
  • Semigroup of isometries
  • Toeplitz algebra

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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