Group Actions on Product Systems

Group Actions on Product Systems

We introduce the concept of a crossed product of a product system by a locally compact group. We prove that the crossed product of a row-finite and faithful product system by an amenable group is also a row-finite and faithful product system. We generalize a theorem of Hao and Ng about the crossed p...

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Veröffentlicht in:New Zealand journal of mathematics 2023-10, Vol.54, p.33-47
Hauptverfasser: Deaconu, Valentin, Huang, Leonard
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Huang, Leonard
description We introduce the concept of a crossed product of a product system by a locally compact group. We prove that the crossed product of a row-finite and faithful product system by an amenable group is also a row-finite and faithful product system. We generalize a theorem of Hao and Ng about the crossed product of the Cuntz-Pimsner algebra of a $C^{\ast}$-correspondence by a group action to the context of product systems. We present examples related to group actions on $k$-graphs and to higher rank Doplicher-Roberts algebras.
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