### 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) |
---|---|

Pages (from-to) | 419-453 |

Number of pages | 35 |

Journal | Communications in Mathematical Physics |

Volume | 244 |

Issue number | 3 |

DOIs | |

State | Published - Feb 2004 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Exponential Equations Related to the Quantum 'ax + b' Group.** / Rowicka-Kudlicka, Malgorzata.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 244, no. 3, pp. 419-453. https://doi.org/10.1007/s00220-003-1010-6

}

TY - JOUR

T1 - Exponential Equations Related to the Quantum 'ax + b' Group

AU - Rowicka-Kudlicka, Malgorzata

PY - 2004/2

Y1 - 2004/2

N2 - We study pairs b, β of unbounded selfadjoint operators, satisfying commutation rules inspired by the quantum 'ax + b' group [19]: bβ = -βb and β2= 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.

AB - We study pairs b, β of unbounded selfadjoint operators, satisfying commutation rules inspired by the quantum 'ax + b' group [19]: bβ = -βb and β2= 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.

UR - http://www.scopus.com/inward/record.url?scp=1142300705&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1142300705&partnerID=8YFLogxK

U2 - 10.1007/s00220-003-1010-6

DO - 10.1007/s00220-003-1010-6

M3 - Article

VL - 244

SP - 419

EP - 453

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -