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Maximal Coactions

Siegfried Echterhoff·S. Kaliszewski·John Quigg
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Abstract

A coaction d of a locally compact group G on a C*-algebra A is maximal if a certain natural map from A times_d G times_{d hat} G onto A otimes K(L^2(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.

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Siegfried Echterhoff, S. Kaliszewski, John Quigg. 2001-09-19. Maximal Coactions. https://arxiv.org/abs/math/0109137

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