Crossed products and C*-covers of semi-Dirichlet operator algebras
Operator Algebras
2025-03-20 v2
Abstract
In this paper, we show that the semi-Dirichlet C*-covers of a semi-Dirichlet operator algebra form a complete lattice, establishing that there is a maximal semi-Dirichlet C*-cover. Given an operator algebra dynamical system we prove a dilation theory that shows that the full crossed product is isomorphic to the relative full crossed product with respect to this maximal semi-Dirichlet cover. In this way, we can show that every semi-Dirichlet dynamical system has a semi-Dirichlet full crossed product.
Keywords
Cite
@article{arxiv.2309.16130,
title = {Crossed products and C*-covers of semi-Dirichlet operator algebras},
author = {Adam Humeniuk and Elias G. Katsoulis and Christopher Ramsey},
journal= {arXiv preprint arXiv:2309.16130},
year = {2025}
}
Comments
Final version, very minor typographical changes. Accepted to Documenta Math