### 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(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.

Original language | English (US) |
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Pages (from-to) | 47-61 |

Number of pages | 15 |

Journal | International Journal of Mathematics |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1 2004 |

### Keywords

- C*-algebra
- Coaction
- Crossed product
- Duality
- Locally compact group

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Echterhoff, S., Kaliszewski, S., & Quigg, J. (2004). Maximal coactions.

*International Journal of Mathematics*,*15*(1), 47-61. https://doi.org/10.1142/S0129167X04002107