Maximal coactions

Siegfried Echterhoff; Steven Kaliszewski; John Quigg

doi:10.1142/S0129167X04002107

Maximal coactions

Siegfried Echterhoff, Steven Kaliszewski, John Quigg

Mathematical and Statistical Sciences, School of (SoMSS)

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

32 Scopus citations

Abstract

A coaction δ of a locally compact group G on a C*-algebra A is maximal if a certain natural map from A x _δ G x _δ G onto A⊗K(L²(G)) is an isomorphism. All dual coactions on full crossed products by group actions are maximal; a discrete coaction is maximal if and only if A is the full cross-sectional algebra of the corresponding Fell bundle. For every nondegenerate coaction of G on A, there is a maximal coaction of G on an extension of A such that the quotient map induces an isomorphism of the crossed products.

Original language	English (US)
Pages (from-to)	47-61
Number of pages	15
Journal	International Journal of Mathematics
Volume	15
Issue number	1
DOIs	https://doi.org/10.1142/S0129167X04002107
State	Published - Feb 2004

Keywords

C*-algebra
Coaction
Crossed product
Duality
Locally compact group

ASJC Scopus subject areas

Mathematics(all)

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10.1142/S0129167X04002107

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title = "Maximal coactions",

abstract = "A coaction δ of a locally compact group G on a C*-algebra A is maximal if a certain natural map from A x δ G x δ G onto A⊗K(L2(G)) is an isomorphism. All dual coactions on full crossed products by group actions are maximal; a discrete coaction is maximal if and only if A is the full cross-sectional algebra of the corresponding Fell bundle. For every nondegenerate coaction of G on A, there is a maximal coaction of G on an extension of A such that the quotient map induces an isomorphism of the crossed products.",

keywords = "C*-algebra, Coaction, Crossed product, Duality, Locally compact group",

author = "Siegfried Echterhoff and Steven Kaliszewski and John Quigg",

note = "Funding Information: Parts of this research were accomplished during separate visits of the second and third authors to the first. The second two authors are grateful to their hosts, and especially to Joachim Cuntz, for their generous hospitality during their respective visits. This research was partially supported by Deutsche Forschungsgemeinschaft (SFB 478).",

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AU - Echterhoff, Siegfried

AU - Kaliszewski, Steven

AU - Quigg, John

N1 - Funding Information: Parts of this research were accomplished during separate visits of the second and third authors to the first. The second two authors are grateful to their hosts, and especially to Joachim Cuntz, for their generous hospitality during their respective visits. This research was partially supported by Deutsche Forschungsgemeinschaft (SFB 478).

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Y1 - 2004/2

N2 - A coaction δ of a locally compact group G on a C*-algebra A is maximal if a certain natural map from A x δ G x δ G onto A⊗K(L2(G)) is an isomorphism. All dual coactions on full crossed products by group actions are maximal; a discrete coaction is maximal if and only if A is the full cross-sectional algebra of the corresponding Fell bundle. For every nondegenerate coaction of G on A, there is a maximal coaction of G on an extension of A such that the quotient map induces an isomorphism of the crossed products.

AB - A coaction δ of a locally compact group G on a C*-algebra A is maximal if a certain natural map from A x δ G x δ G onto A⊗K(L2(G)) is an isomorphism. All dual coactions on full crossed products by group actions are maximal; a discrete coaction is maximal if and only if A is the full cross-sectional algebra of the corresponding Fell bundle. For every nondegenerate coaction of G on A, there is a maximal coaction of G on an extension of A such that the quotient map induces an isomorphism of the crossed products.

KW - C-algebra

KW - Coaction

KW - Crossed product

KW - Duality

KW - Locally compact group

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JF - International Journal of Mathematics

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Maximal coactions

Abstract

Keywords

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