Compact Ergodic Groups of Automorphisms

Høegh-Krohn, Raphaël; Landstad, Magnus B.; Størmer, Erling

doi:10.2307/1971377

Cited by 85 publications

(103 citation statements)

References 12 publications

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“…If € is an ergodic coaction of G on A (1 e A) Corresponding to the results of Hoegh-Krohn, Landstad and Stormer (see [5]), we have the following results. PROPOSITION …”

Section: Proof For Any (N H) E a Let (mentioning

confidence: 83%

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Discrete coactions on C*-algebras

1996

J Aust Math Soc A

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We will consider coactions of discrete groups on C*-algebras and imitate some of the results about compact group actions on C*-algebras. In particular, the crossed product of a reduced coaction e of a discrete amenable group G on A is liminal (respectively, postliminal) if and only if the fixed point algebra of e is. Moreover, we will also consider ergodic coactions on C* -algebras.1991 Mathematics subject classification (Amer. Math. Soc): 46L55.

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“…If € is an ergodic coaction of G on A (1 e A) Corresponding to the results of Hoegh-Krohn, Landstad and Stormer (see [5]), we have the following results. PROPOSITION …”

Section: Proof For Any (N H) E a Let (mentioning

confidence: 83%

“…As a corollary, we show that if the fixed point algebra is postliminal, then the original algebra is nuclear. In Section 4, we try to translate some results in the paper [5] [2]…”

Section: Introduction and Notationmentioning

confidence: 99%

Discrete coactions on C*-algebras

1996

J Aust Math Soc A

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“…We study spectral subspaces and prove in particular that they are finite dimensional. The results in this section are well known (see [16] for the classical case of compact groups and [10,18,23] for compact quantum groups). We give a short presentation for the convenience of the reader.…”

Section: Spectral Subspaces and Quantum Multiplicitymentioning

confidence: 88%

Ergodic Coactions with Large Multiplicity and Monoidal Equivalence of Quantum Groups

Bichon

Rijdt

Vaes

2005

Commun. Math. Phys.

120

303

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We construct new examples of ergodic coactions of compact quantum groups, in which the multiplicity of an irreducible corepresentation can be strictly larger than the dimension of the latter. These examples are obtained using a bijective correspondence between certain ergodic coactions on C * -algebras and unitary fiber functors on the representation category of a compact quantum group. We classify these unitary fiber functors on the universal orthogonal and unitary quantum groups. The associated C * -algebras and von Neumann algebras can be defined by generators and relations, but are not yet well understood.

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“…The proof can be obtained by combining the results of [7], [4] and [1]. Let now h = L 2 (A, τ ), where τ is the unique invariant faithful trace described in Proposition 2.1.…”

Section: Proposition 21 Let G Be a Compact Group Acting Ergodically mentioning

confidence: 95%

On equivariant embedding of Hilbert C* modules

Goswami

2009

Proc Math Sci

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Compact Ergodic Groups of Automorphisms

Abstract: It is shown that if G is a compact ergodic group of -automorphisms on a unital c-algebra A then the un1que G-invariant state is a trace. Hence if A is a von Neumann algebra then it is finite.

Cited by 85 publications

References 12 publications

Discrete coactions on C*-algebras

Discrete coactions on C*-algebras

Ergodic Coactions with Large Multiplicity and Monoidal Equivalence of Quantum Groups

On equivariant embedding of Hilbert C* modules

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Compact Ergodic Groups of Automorphisms

Abstract: It is shown that if G is a compact ergodic group of *-automorphisms on a unital c*-algebra A then the un1que G-invariant state is a trace. Hence if A is a von Neumann algebra then it is finite.

Cited by 85 publications

References 12 publications

Discrete coactions on C*-algebras

Discrete coactions on C*-algebras

Ergodic Coactions with Large Multiplicity and Monoidal Equivalence of Quantum Groups

On equivariant embedding of Hilbert C* modules

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Product

Resources

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Abstract: It is shown that if G is a compact ergodic group of -automorphisms on a unital c-algebra A then the un1que G-invariant state is a trace. Hence if A is a von Neumann algebra then it is finite.