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:Journal of functional analysis 2020-11, Vol.279 (9), p.108731, Article 108731
Main Author: Humeniuk, Adam
Format: Article
Language:English
Subjects:
C-envelope
Crossed product
Nica-covariant
Semicrossed product
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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 Z+n to the class of all discrete lattice ordered abelian groups.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2020.108731