Journal of Operator Theory

Volume 44, Issue 1, Summer 2000 pp. 139-150.

Semigroup crossed products and the structure of Toeplitz algebras

Authors: Sriwulan Adji
Author institution: Department of Mathematics, Bandung Institute of Technology, Bandung 40132, Indonesia

Summary: Suppose

$\Gamma$ is a totally ordered discrete abelian group, and

$I$ is an ordered ideal in

$\Gamma$ . We show that the crossed product

$A\times \Gamma^+$ by an action inflated from one

$\Gamma/I$ is isomorphic to the induced algebra

$\ind^{\widehat\Gamma}_{I^\bot}A \times (\Gamma/I)^+$ . Using this we show how the

$\wgamma$ -invariant ideals in the Toeplitz algebra of

$\Gamma$ are determined by the order ideals in

$\Gamma$ .

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