Journal of Operator Theory

Volume 79, Issue 2, Spring 2018 pp. 403-418.

The Jacobson radical of certain semicrossed products

Authors: Jaspar Wiart
Author institution: Department of Pure Mathematics, University of Waterloo, Waterloo, N2L 3G1, Canada

Summary: We study the Jacobson radical of the semicrossed product $\mathcal{A}\times_\alpha~P$ when $\mathcal {A}$ is a simple $C^*$-algebra and $P$ is either a semigroup contained in an abelian group or a free semigroup. A full characterization is obtained for a large subset of these semicrossed products and we apply our results to a number of examples.

DOI: http://dx.doi.org/10.7900/jot.2017may02.2159
Keywords: semicrossed product, endomorphism, dynamical system, $C^*$-algebra, finite index conditional expectation, Jacobson radical, semi-simplicity, purely infinite

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