Ergodic invariant states and irreducible representations of crossed product C*-algebras

Huichi Huang; Jianchao Wu

doi:10.7900/jot.2016jun11.2141

Ergodic invariant states and irreducible representations of crossed product C*-algebras

Huichi Huang
, Jianchao Wu

Mathematics

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

5 Scopus citations

Abstract

Motivated by reformulating Furstenberg's ×p,×q conjecture via representations of a crossed product C*-algebra, we show that in a discrete C*-dynamical system (A, Γ), the space of (ergodic) Γ-invariant states on A is homeomorphic to a subspace of (pure) state space of A ⋊ Γ. Various applications of this in topological dynamical systems and representation theory are obtained.

Original language	English (US)
Pages (from-to)	159-172
Number of pages	14
Journal	Journal of Operator Theory
Volume	78
Issue number	1
DOIs	https://doi.org/10.7900/jot.2016jun11.2141
State	Published - Jun 1 2017

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.7900/jot.2016jun11.2141

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abstract = "Motivated by reformulating Furstenberg's ×p,×q conjecture via representations of a crossed product C*-algebra, we show that in a discrete C*-dynamical system (A, Γ), the space of (ergodic) Γ-invariant states on A is homeomorphic to a subspace of (pure) state space of A ⋊ Γ. Various applications of this in topological dynamical systems and representation theory are obtained.",

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N2 - Motivated by reformulating Furstenberg's ×p,×q conjecture via representations of a crossed product C*-algebra, we show that in a discrete C*-dynamical system (A, Γ), the space of (ergodic) Γ-invariant states on A is homeomorphic to a subspace of (pure) state space of A ⋊ Γ. Various applications of this in topological dynamical systems and representation theory are obtained.

AB - Motivated by reformulating Furstenberg's ×p,×q conjecture via representations of a crossed product C*-algebra, we show that in a discrete C*-dynamical system (A, Γ), the space of (ergodic) Γ-invariant states on A is homeomorphic to a subspace of (pure) state space of A ⋊ Γ. Various applications of this in topological dynamical systems and representation theory are obtained.

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JO - Journal of Operator Theory

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Ergodic invariant states and irreducible representations of crossed product C*-algebras

Abstract

All Science Journal Classification (ASJC) codes

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