Communications in Mathematical Physics

, Volume 244, Issue 3, pp 419–453

Exponential Equations Related to the Quantum ‘ax + b’ Group


DOI: 10.1007/s00220-003-1010-6

Cite this article as:
Rowicka, M. Commun. Math. Phys. (2004) 244: 419. doi:10.1007/s00220-003-1010-6


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 β2=0. We find all measurable, unitary-operator valued functions F satisfying the exponential equation: F(b, β)F(d, δ)=F((b, β) (d, δ)), where d, δ satisfy the same commutation rules as b, β, and 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 [12].

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of Mathematical Methods in PhysicsUniversity of WarsawWarsawPoland
  2. 2.University of Texas SouthwesternDallasUSA

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