### Abstract

We study pairs b, β of unbounded selfadjoint operators, satisfying commutation rules inspired by the quantum 'ax + b' group [19]: bβ = -βb and β^{2}= id except for kerb, on which β ^{2} = 0. We find all measurable, unitary-operator valued functions F satisfying the exponential equation: F(b, β)F(d, δ) = F((b, β) circled inside astrik sign (d, δ)), where d, δ satisfy the same commutation rules as b, β, and cirlcle astrik sign is modeled after the comultiplication of the quantum 'ax + b' group. This result is crucial for classification of all unitary representations of the quantum 'ax + b' group, which is achieved in our forthcoming paper.

Original language | English (US) |
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Pages (from-to) | 419-453 |

Number of pages | 35 |

Journal | Communications in Mathematical Physics |

Volume | 244 |

Issue number | 3 |

DOIs | |

State | Published - Feb 1 2004 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics