C*-envelopes of semicrossed products by lattice ordered abelian semigroups
arXiv, 2020
Online
unknown
Zugriff:
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.
Comment: 36 pages. Updated to reflect published version in JFA. Minor typos fixed throughout and new Corollary 3.18 (nonunital case) and Subsection 6.1 (simplicity of the C*-envelope) added
Titel: |
C*-envelopes of semicrossed products by lattice ordered abelian semigroups
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Autor/in / Beteiligte Person: | Humeniuk, Adam |
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Veröffentlichung: | arXiv, 2020 |
Medientyp: | unknown |
DOI: | 10.48550/arxiv.2001.07294 |
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