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Coactions and skew products for topological quivers

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  22 May 2024

Lucas Hall Open the ORCID record for Lucas Hall [Opens in a new window]
Lucas Hall*
Affiliation:
Department of Mathematics, University of Haifa, Haifa, Israel Department of Mathematics, Michigan State University, East Lansing, Michigan, US
*
Email: hallluc1@msu.edu
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Abstract

Given a cocycle on a topological quiver by a locally compact group, the author constructs a skew product topological quiver and determines conditions under which a topological quiver can be identified as a skew product. We investigate the relationship between the ${C^*}$-algebra of the skew product and a certain native coaction on the ${C^*}$-algebra of the original quiver, finding that the crossed product by the coaction is isomorphic to the skew product. As an application, we show that the reduced crossed product by the dual action is Morita equivalent to the ${C^*}$-algebra of the original quiver.

Keywords

G-bundlecrossed productcoactiontopological quiver

MSC classification

Primary: 46L55: Noncommutative dynamical systems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 67 , Issue 3 , August 2024 , pp. 921 - 946
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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