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Semicrossed Products, Dilations, and Jacobson Radicals

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Wiart_Jaspar.pdf (401.38 KB)

Date

2017-08-18

Authors

Wiart, Jaspar

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University of Waterloo

Abstract

We compute the C*-envelope of the isometric semicrossed product of a C*-algebra arising from number theory by the multiplicative semigroup of a number ring R, and prove that it is isomorphic to T[R], the left regular representation of the ax+b-semigroup of R. We do this by explicitly dilating an arbitrary representation of the isometric semicrossed product to a representation of T[R] and show that such representations are maximal. We also study the Jacobson radical of the semicrossed product of a simple C*-algebra and either a subsemigroup of an abelian group or a free semigroup. A full characterization of the Jacobson radical is obtained for a large subset of these semicrossed products and we apply our results to a number of examples.

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Keywords

Semicrossed product, C*-algebra, C*-envelope, Dilation, Dynamical System, Endomorphism, Finite Index Conditional Expectation, Jacobson Radical, Purely Infinite, Semi-simplicity

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http://hdl.handle.net/10012/12159

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Pure Mathematics