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arXiv · 2309.16130

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

Adam Humeniuk·Elias G. Katsoulis·Christopher Ramsey
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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.

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Adam Humeniuk, Elias G. Katsoulis, Christopher Ramsey. 2025-03-19. Crossed products and C*-covers of semi-Dirichlet operator algebras. https://arxiv.org/abs/2309.16130

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