Communications in Mathematical Physics

, Volume 244, Issue 3, pp 419–453 | Cite as

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

Article

Abstract

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].

Keywords

Unitary Representation Forthcoming Paper Selfadjoint Operator Exponential Equation Kerb 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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