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arXiv · 2503.09043

Takai duality and crossed product hosts in C*-actions

Yusuke Nakae
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Abstract

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.

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Yusuke Nakae. 2025-05-10. Takai duality and crossed product hosts in C*-actions. https://arxiv.org/abs/2503.09043

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