Product systems over Ore monoids

Albandik, Suliman; Meyer, Ralf

doi:10.4171/dm/521

Cited by 16 publications

(2 citation statements)

References 60 publications

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“…we see that S is a C * -isomorphism, and as g is arbitrary and β is an action of G on Y, there is an action γ of G on O(Y) that satisfies (1). The strong continuity of γ immediately follows from the continuity of j Y and the strong continuity of each β p .…”

Section: A⋊αgmentioning

confidence: 89%

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Group Actions on Product Systems

Deaconu,

Huang

2023

NZ J Math

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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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Section: A⋊αgmentioning

confidence: 89%

“…Product systems over various discrete semigroups P were introduced by N. Fowler in [7], inspired by work of W. Arveson and studied by several authors (see [1,3,16], for example). Several interesting examples of product systems already occur over the semigroup N k , + , where k ≥ 2, for example product systems associated to k-graphs.…”

Section: Introductionmentioning

confidence: 99%

Group Actions on Product Systems

Deaconu,

Huang

2023

NZ J Math

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Product systems of C*-correspondences and Takai duality

Katsoulis

2020

Isr. J. Math.

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On C⁎-algebras associated to product systems

Sehnem

2019

Journal of Functional Analysis

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Let P be a unital subsemigroup of a group G. We propose an approach to C * -algebras associated to product systems over P . We call the C * -algebra of a given product system E its covariance algebra and denote it by A× E P , where A is the coefficient C * -algebra. We prove that our construction does not depend on the embedding P → G and that a representation of A × E P is faithful on the fixed-point algebra for the canonical coaction of G if and only if it is faithful on A. We compare this with other constructions in the setting of irreversible dynamical systems, such as Cuntz-Nica-Pimsner algebras, Fowler's Cuntz-Pimsner algebra, semigroup C * -algebras of Xin Li and Exel's crossed products by interaction groups.

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Product systems over Ore monoids

Cited by 16 publications

References 60 publications

Group Actions on Product Systems

Group Actions on Product Systems

Product systems of C*-correspondences and Takai duality

On C⁎-algebras associated to product systems

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