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C*-Envelope and Dilation Theory of Semigroup Dynamical Systems

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Abstract

In this paper, we construct, for a certain class of semigroup dynamical systems, two operator algebras that are universal with respect to their corresponding covariance conditions: one being selfadjoint, and another being nonselfadjoint. We prove that the C*-envelope of the nonselfadjoint operator algebra is precisely the selfadjoint one. This result leads to a number of new examples of operator algebras and their C*-envelopes, with many from number fields and commutative rings. We further establish the functoriality of these operator algebras along with their applications.

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  1. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada

    Boyu Li

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The author was supported by a fellowship of the Pacific Institute for the Mathematical Sciences.

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Li, B. C*-Envelope and Dilation Theory of Semigroup Dynamical Systems. Integr. Equ. Oper. Theory 93, 19 (2021). https://doi.org/10.1007/s00020-021-02636-6

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  • DOI: https://doi.org/10.1007/s00020-021-02636-6

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