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arXiv · 2001.07294

C*-envelopes of semicrossed products by lattice ordered abelian semigroups

Adam Humeniuk
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Abstract

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.

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Adam Humeniuk. 2020-01-21. C*-envelopes of semicrossed products by lattice ordered abelian semigroups. https://doi.org/10.1016/j.jfa.2020.108731

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