Communications in Mathematical Physics

, Volume 136, Issue 2, pp 399–432 | Cite as

Unbounded elements affiliated withC*-algebras and non-compact quantum groups

  • S. L. Woronowicz
Article

Abstract

The affiliation relation that allows to include unbounded elements (operators) into theC*-algebra framework is introduced, investigated and applied to the quantum group theory. The quantum deformation of (the two-fold covering of) the group of motions of Euclidean plane is constructed. A remarkable radius quantization is discovered. It is also shown that the quantumSU(1, 1) group does not exist on theC*-algebra level for real value of the deformation parameter.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Group Theory 

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • S. L. Woronowicz
    • 1
  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

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