### Abstract

We show that for a locally compact group G there is a one-to-one correspondence between G-invariant weak*-closed subspaces E of the Fourier-Stieltjes algebra B(G) containing B_{r}(G) and quotients C*_{E} (G) of C*(G) which are intermediate between C*(G) and the reduced group algebra C*_{r} (G). We show that the canonical comultiplication on C*(G) descends to a coaction or a comultiplication on C*_{E} (G) if and only if E is an ideal or subalgebra, respectively. When α is an action of G on a C*-algebra B, we define E-crossed products B ⋊ α,E G lying between the full crossed product and the reduced one, and we conjecture that these intermediate crossed products satisfy an exotic version of crossed-product duality involving C*_{E} (G).

Original language | English (US) |
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Pages (from-to) | 689-711 |

Number of pages | 23 |

Journal | New York Journal of Mathematics |

Volume | 19 |

State | Published - Nov 7 2013 |

### Keywords

- C*-bialgebra
- Coaction
- Fourier-stieltjes algebra
- Group C*-algebra
- Hopf C*-algebra
- Quantum group

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*New York Journal of Mathematics*,

*19*, 689-711.