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• W3160451608 abstract "We consider groupoids constructed from a finite number of commuting local homeomorphisms acting on a compact metric space, and study generalized Ruelle operators and $ C^{ast} $-algebras associated to these groupoids. We provide a new characterization of $ 1 $-cocycles on these groupoids taking values in a locally compact abelian group, given in terms of $ k $-tuples of continuous functions on the unit space satisfying certain canonical identities. Using this, we develop an extended Ruelle-Perron-Frobenius theory for dynamical systems of several commuting operators ($ k $-Ruelle triples and commuting Ruelle operators). Results on KMS states on $ C^{ast} $-algebras constructed from these groupoids are derived. When the groupoids being studied come from higher-rank graphs, our results recover existence-uniqueness results for KMS states associated to the graphs." @default.
• W3160451608 created "2021-05-24" @default.
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• W3160451608 date "2020-10-06" @default.
• W3160451608 modified "2023-09-27" @default.
• W3160451608 title "Cocycles on Certain Groupoids Associated to $ mathbb{N}^{k} $-Actions" @default.
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• W3160451608 hasPublicationYear "2020" @default.
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