Crossed products and -covers of semi-Dirichlet operator algebras
Adam Humeniuk
Mount Royal University, Calgary, AB, CanadaElias G. Katsoulis
East Carolina University, Greenville, USAChristopher Ramsey
MacEwan University, Edmonton, AB, Canada

Abstract
In this paper, we show that the semi-Dirichlet -covers of a semi-Dirichlet operator algebra form a complete lattice, establishing that there is a maximal semi-Dirichlet -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.
Cite this article
Adam Humeniuk, Elias G. Katsoulis, Christopher Ramsey, Crossed products and -covers of semi-Dirichlet operator algebras. Doc. Math. 30 (2025), no. 4, pp. 909–933
DOI 10.4171/DM/1007