Semigroup crossed products and the induced algebras of lattice-ordered groups

Mamoon Ali Ahmed, Alan James Pryde

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

Let (G, G(+)) be a quasi-lattice-ordered group with positive cone G(+). Laca and Raeburn have shown that the universal C*-algebra C*(G, G(+)) introduced by Nica is a crossed product BG+ x(alpha) G(+) by a semigroup of endomorphisms. The goal of this paper is to extend some results for totally ordered abelian groups to the case of discrete lattice-ordered abelian groups. In particular given a hereditary subsemigroup H+ of G(+) we introduce a closed ideal IH+ of the C*-algebra BG+. We construct an approximate identity for this ideal and show that IH+ is extendibly alpha-invariant. It follows that there is an isomorphism between C*-crossed products (BG+/IH+) x (alpha) over tilde, G+ and B(G/H)+ x(beta) G(+). This leads to our main result that B(G/H)+ x(beta) G(+) is realized as an induced C*-algebra Ind(H(sic))((G) over cap) (B(G/H)+ x(tau) (G/H)(+)).
Original languageEnglish
Pages (from-to)498 - 507
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Volume364
Issue number2
Publication statusPublished - 2010

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