Crossed products of operator systems

Abstract

In this paper we introduce the crossed product construction for a discrete group action on an operator system. In analogy to the work of E. Katsoulis and C. Ramsey, we describe three canonical crossed products arising from such a dynamical system. We describe how these crossed product constructions behave under $G$-equivariant maps, tensor products, and the canonical $C^{\ast }$-covers. We show that hyperrigidity is preserved under two of the three crossed products. Finally, using A. Kavruk's notion of an operator system that detects $C^{\ast }$-nuclearity, we give a negative answer to a question on operator algebra crossed products posed by Katsoulis and Ramsey.

arXiv comment31 pages. Final version to appear in the Journal of Functional Analysis

References in corpus (7)

• The noncommutative Choquet boundary
• Uniformly recurrent subgroups and the ideal structure of reduced crossed products
• Nuclearity-related properties for nonselfadjoint algebras
• The classification problem for finitely generated operator systems and spaces
• Extensions of operator algebras I
• Existence of tracial states on reduced group C*-algebras
• Operator System Nuclearity via $C^{\ast }$-envelopes