C-envelopes of semicrossed products by lattice ordered abelian semigroups

A semicrossed product is a non-selfadjoint operator algebra encoding the action of a semigroup on an operator or C*-algebra. We prove that, when the positive cone of a discrete lattice ordered abelian group acts on a C*-algebra, the C*-envelope of the associated semicrossed product is a full corner...

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Bibliographic Details
Published in:arXiv.org 2021-02
Main Author: Humeniuk, Adam
Format: Article
Language:English
Subjects:
Algebra
Group theory
Online Access:Get full text
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Summary:A semicrossed product is a non-selfadjoint operator algebra encoding the action of a semigroup on an operator or C*-algebra. We prove that, when the positive cone of a discrete lattice ordered abelian group acts on a C*-algebra, the C*-envelope of the associated semicrossed product is a full corner of a crossed product by the whole group. By constructing a C*-cover that itself is a full corner of a crossed product, and computing the Shilov ideal, we obtain an explicit description of the C*-envelope. This generalizes a result of Davidson, Fuller, and Kakariadis from \(\mathbb{Z}_+^n\) to the class of all discrete lattice ordered abelian groups.
ISSN:2331-8422
DOI:10.48550/arxiv.2001.07294