Crossed products of operator algebras
crossed product, Jacobson Radical, semicrossed product, Takai duality
We study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. We develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. We complement our generic results with the detailed study of many important special cases. In particular we study crossed products of tensor algebras, triangular AF algebras and various associated C°-algebras. We make contributions to the study of C°-envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. We also answer questions from the pertinent literature.
Katsoulis, E. and C. Ramsey. (2019). Crossed products of operator algebras. American Mathematical Society. https://arxiv.org/abs/1512.08162
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