On Hong and Szymański’s Description of the Primitive-Ideal Space of a Graph Algebra

Carlsen, Toke Meier; Sims, Aidan

doi:10.1007/978-3-319-39286-8_4

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Graph Algebras1

The Jacobson Topology1

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2020

2021

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Article2

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Cited by 3 publications

(2 citation statements)

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“…In this section we propose an equivalent description obtained entirely using the groupoid picture for these C * -algebras. For the case of row-finite graphs without sources, see also [CS17,BCS23].…”

Section: Graph Algebrasmentioning

confidence: 99%

(Non)exotic Completions of the Group Algebras of Isotropy Groups

Christensen

Neshveyev

2021

International Mathematics Research Notices

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Motivated by the problem of characterizing KMS states on the reduced C$^*$-algebras of étale groupoids, we show that the reduced norm on these algebras induces a C$^*$-norm on the group algebras of the isotropy groups. This C$^*$-norm coincides with the reduced norm for the transformation groupoids, but, as follows from examples of Higson–Lafforgue–Skandalis, it can be exotic already for groupoids of germs associated with group actions. We show that the norm is still the reduced one for some classes of graded groupoids, in particular, for the groupoids associated with partial actions of groups and the semidirect products of exact groups and groupoids with amenable isotropy groups.

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Section: Graph Algebrasmentioning

confidence: 99%

(Non)exotic Completions of the Group Algebras of Isotropy Groups

Christensen

Neshveyev

2021

International Mathematics Research Notices

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“…In this section, we describe the Jacobson topology of the primitive ideal space of self-similar k-graph C*-algebras under certain conditions. Our approach is inspired by [5] and [2].…”

Section: The Jacobson Topologymentioning

confidence: 99%