### Abstract

By weakening the counit and antipode axioms of a C^{*}-Hopf algebra and allowing for the coassociative coproduct to be nonunital, we obtain a quantum group, that we call a weak ^{C*}-Hopf algebra, which is sufficiently general to describe the symmetries of essentially arbitrary fusion rules. This amounts to generalizing the Baaj-Skandalis multiplicative unitaries to multipicative partial isometrics. Every finite-dimensional weak C^{*}-Hopf algebra has a dual which is again a weak C^{*}-Hopf algebra. An explicit example is presented with Lee-Yang fusion rules. We briefly discuss applications to amalgamated crossed products, doubles, and quantum chains.

Original language | English |
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Pages (from-to) | 437-456 |

Number of pages | 20 |

Journal | Letters in Mathematical Physics |

Volume | 38 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 1996 |

### Keywords

- Amalgamated crossed products
- Multiplicative isometrics
- Weak Hopf algebras

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Bòhm, G., & Szlachónyi, K. (1996). A Coassociative C-Quantum Group with Nonintegral Dimensions.

*Letters in Mathematical Physics*,*38*(4), 437-456. https://doi.org/10.1007/BF01815526