Semicrossed Products, Dilations, and Jacobson Radicals

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

Wiart, Jasparadvisor:Ken, Davidson ; affiliation1:Faculty of Mathematics ; Ken, Davidson ;

University of Waterloo

关键词: Jacobson Radical;    Semicrossed product;    Finite Index Conditional Expectation;    Endomorphism;    Purely Infinite;    C*-envelope;    Dynamical System;    C*-algebra;    Dilation;    Semi-simplicity;    Doctoral Thesis;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/12159/1/Wiart_Jaspar.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

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.