2025/03/12 by Yusuke Nakae, Nakae, Yusuke
Computer Science · #22D25 #46L55 #47L65 #81R15 #Advanced Algebra and Logic #FOS: Mathematics #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2503.09043
openalex publication_date 2025/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Crossed product algebras are fundamental in the study of C*-algebras, traditionally under the assumption of continuity of group actions. Recent work by Grundling and Neeb introduced the crossed product host, an analog of the crossed product for a singular action. In this paper, we investigate the structure of the crossed product host and its relation to the conventional crossed product. We examine the validity of Takai-type duality in this setting and establish connections via the Landstad algebra. Additionally, we provide a necessary and sufficient condition for the existence of ground states, and show that for amenable groups, if the full and reduced crossed product hosts exist, then they coincide.