Communications in Mathematical Physics

, Volume 136, Issue 2, pp 399–432

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


  • S. L. Woronowicz
    • Research Institute for Mathematical SciencesKyoto University

DOI: 10.1007/BF02100032

Cite this article as:
Woronowicz, S.L. Commun.Math. Phys. (1991) 136: 399. doi:10.1007/BF02100032


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.

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© Springer-Verlag 1991