Crossed products and C*-covers of semi-Dirichlet operator algebras

2023/09/28 by Humeniuk, Adam, Katsoulis, Elias G., Ramsey, Christopher · 1 citation
#46L05 #47L55 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2309.16130

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.

Cited by

• Couniversality for C*-algebras of residually finite-dimensional operator algebras

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• Admissibility of C*-Covers for Operator Algebra Dynamical Systems
• Dilation theory, commutant lifting and semicrossed products
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