On simplicity of intermediate -algebras

Tattwamasi Amrutam; Mehrdad Kalantar

doi:10.1017/etds.2019.34

On simplicity of intermediate -algebras

Tattwamasi Amrutam, Mehrdad Kalantar

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We prove simplicity of all intermediate -algebras in the case of minimal actions of -simple groups on compact spaces. For this, we use the notion of stationary states, recently introduced by Hartman and Kalantar [Stationary -dynamical systems. Preprint, 2017, arXiv:1712.10133]. We show that the Powers' averaging property holds for the reduced crossed product for any action of a -simple group on a unital -algebra, and use it to prove a one-to-one correspondence between stationary states on and those on.

Original language	English
Pages (from-to)	3181-3187
Number of pages	7
Journal	Ergodic Theory and Dynamical Systems
Volume	40
Issue number	12
DOIs	https://doi.org/10.1017/etds.2019.34
State	Published - 1 Dec 2020
Externally published	Yes

Keywords

37A55
46L10
46L55 (Primary)
46L89 (Secondary)
C-simplicity 2010 Mathematics Subject Classification
crossed product C-algebras
group actions
operator algebras
stationary group actions

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1017/etds.2019.34

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title = "On simplicity of intermediate -algebras",

abstract = "We prove simplicity of all intermediate -algebras in the case of minimal actions of -simple groups on compact spaces. For this, we use the notion of stationary states, recently introduced by Hartman and Kalantar [Stationary -dynamical systems. Preprint, 2017, arXiv:1712.10133]. We show that the Powers' averaging property holds for the reduced crossed product for any action of a -simple group on a unital -algebra, and use it to prove a one-to-one correspondence between stationary states on and those on.",

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AU - Kalantar, Mehrdad

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AB - We prove simplicity of all intermediate -algebras in the case of minimal actions of -simple groups on compact spaces. For this, we use the notion of stationary states, recently introduced by Hartman and Kalantar [Stationary -dynamical systems. Preprint, 2017, arXiv:1712.10133]. We show that the Powers' averaging property holds for the reduced crossed product for any action of a -simple group on a unital -algebra, and use it to prove a one-to-one correspondence between stationary states on and those on.

KW - 37A55

KW - 46L10

KW - 46L55 (Primary)

KW - 46L89 (Secondary)

KW - C-simplicity 2010 Mathematics Subject Classification

KW - crossed product C-algebras

KW - group actions

KW - operator algebras

KW - stationary group actions

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DO - 10.1017/etds.2019.34

M3 - Article

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SN - 0143-3857

VL - 40

SP - 3181

EP - 3187

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 12

ER -

On simplicity of intermediate -algebras

Abstract

Keywords

ASJC Scopus subject areas

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