### Abstract

Using the close relationship between coactions of discrete groups and Fell bundles, we introduce a rocedure for inducing a C*-coaction δ: D → D ⊗ C* (G/N) of a quotient group G/N of a discrete group G to a C*-coaction Ind δ: Ind D → Ind D ⊗ C* (G) of G. We show that induced coactions behave in many respects similarly to induced actions. In particular, as an analogue of the well known imprimitivity theorem for induced actions we prove that the crossed products Ind D ×_{Ind δ} G and D ×_{δ} G/N are always Morita equivalent. We also obtain nonabelian analogues of a theorem of Diesen and Pedersen which show that there is a duality between induced coactions and twisted actions in the sense of Green. We further investigate amenability of Fell bundles corresponding to induced coactions.

Original language | English (US) |
---|---|

Pages (from-to) | 745-770 |

Number of pages | 26 |

Journal | Canadian Journal of Mathematics |

Volume | 51 |

Issue number | 4 |

State | Published - Aug 1999 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Canadian Journal of Mathematics*,

*51*(4), 745-770.

**Induced coactions of discrete groups on C *-algebras.** / Echterhoff, Siegfried; Quigg, John.

Research output: Contribution to journal › Article

*Canadian Journal of Mathematics*, vol. 51, no. 4, pp. 745-770.

}

TY - JOUR

T1 - Induced coactions of discrete groups on C *-algebras

AU - Echterhoff, Siegfried

AU - Quigg, John

PY - 1999/8

Y1 - 1999/8

N2 - Using the close relationship between coactions of discrete groups and Fell bundles, we introduce a rocedure for inducing a C*-coaction δ: D → D ⊗ C* (G/N) of a quotient group G/N of a discrete group G to a C*-coaction Ind δ: Ind D → Ind D ⊗ C* (G) of G. We show that induced coactions behave in many respects similarly to induced actions. In particular, as an analogue of the well known imprimitivity theorem for induced actions we prove that the crossed products Ind D ×Ind δ G and D ×δ G/N are always Morita equivalent. We also obtain nonabelian analogues of a theorem of Diesen and Pedersen which show that there is a duality between induced coactions and twisted actions in the sense of Green. We further investigate amenability of Fell bundles corresponding to induced coactions.

AB - Using the close relationship between coactions of discrete groups and Fell bundles, we introduce a rocedure for inducing a C*-coaction δ: D → D ⊗ C* (G/N) of a quotient group G/N of a discrete group G to a C*-coaction Ind δ: Ind D → Ind D ⊗ C* (G) of G. We show that induced coactions behave in many respects similarly to induced actions. In particular, as an analogue of the well known imprimitivity theorem for induced actions we prove that the crossed products Ind D ×Ind δ G and D ×δ G/N are always Morita equivalent. We also obtain nonabelian analogues of a theorem of Diesen and Pedersen which show that there is a duality between induced coactions and twisted actions in the sense of Green. We further investigate amenability of Fell bundles corresponding to induced coactions.

UR - http://www.scopus.com/inward/record.url?scp=0033439210&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033439210&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033439210

VL - 51

SP - 745

EP - 770

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

SN - 0008-414X

IS - 4

ER -