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)(+)).
|Pages (from-to)||498 - 507|
|Number of pages||10|
|Journal||Journal of Mathematical Analysis and Applications|
|Publication status||Published - 2010|