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

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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.

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Author notes

  1. S. L. Woronowicz

    Present address: Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Hoza 74, PL-00-682, Warszawa, Poland

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  1. Research Institute for Mathematical Sciences, Kyoto University, 606, Kyoto, Japan

    S. L. Woronowicz

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  1. S. L. Woronowicz
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Communicated by H. Araki

Supported by Japan Society for the Promotion of Science

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Woronowicz, S.L. Unbounded elements affiliated withC*-algebras and non-compact quantum groups. Commun.Math. Phys. 136, 399–432 (1991). https://doi.org/10.1007/BF02100032

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  • DOI: https://doi.org/10.1007/BF02100032

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