Crossed Products of Operator Algebras
Abstract
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.
Keywords
Cite
@article{arxiv.1512.08162,
title = {Crossed Products of Operator Algebras},
author = {Elias Katsoulis and Christopher Ramsey},
journal= {arXiv preprint arXiv:1512.08162},
year = {2018}
}
Comments
Several typos corrected. Theorem 3.23 has an easier proof that holds for non-unital algebras as well. A "Note added in proof" at the end of the paper addresses various developments since the last submission to the Arxiv. The paper will appear in the Memoirs of the American Mathematical Society