Ken, DavidsonWiart, Jaspar2017-08-182017-08-182017-08-182017-08-03http://hdl.handle.net/10012/12159We 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.enSemicrossed productC*-algebraC*-envelopeDilationDynamical SystemEndomorphismFinite Index Conditional ExpectationJacobson RadicalPurely InfiniteSemi-simplicityDoctoral Thesis