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Complex quantum groups and their quantum enveloping algebras |
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| Authors: | Bernhard Drabant Michael Schlieker Wolfgang Weich Bruno Zumino |
| Institution: | 1. Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, F?hringer Ring 6, W-8000, München 40, Federal Republic of Germany 2. Sektion Physik der Universit?t München, Lehrstuhl Professor Wess, Theresienstrasse 37, W-8000, München 2, Federal Republic of Germany 3. Department of Physics, University of California, 94720, Berkeley, California, CA, USA |
| Abstract: | We construct complexified versions of the quantum groups associated with the Lie algebras of typeA n?1 ,B n ,C n , andD n . Following the ideas of Faddeev, Reshetikhin and Takhtajan we obtain the Hopf algebras of regular functionals U? on these complexified quantum groups. In the special exampleA 1 we derive theq-deformed enveloping algebraU q (sl(2, ?)). In the limitq→1 the undeformedU q (sl(2, ?)) is recovered. |
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