Crossed products and -covers of semi-Dirichlet operator algebras

  • Adam Humeniuk

    Mount Royal University, Calgary, AB, Canada
  • Elias G. Katsoulis

    East Carolina University, Greenville, USA
  • Christopher Ramsey

    MacEwan University, Edmonton, AB, Canada
Crossed products and $\mathrm{C}^{*}$-covers of semi-Dirichlet operator algebras cover
Download PDF

This article is published open access.

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