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Modular Double of the Quantum Group \(SL_{q}(2, \mathbb{R})\)

  • L. D. Faddeev
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 111)

Abstract

The term “quantum group”, introduced by V. Drinfeld (Proceedings of ICM-86, Berkeley, vol. 1, p. 798. AMS, Providence, 1987), applies in fact to two dual objects: q-deformation of the algebra \(\mathcal{A}\) of functions on the Lie group and that for the universal enveloping algebra \(\mathcal{U}\) of the corresponding Lie algebra. See Faddeev [1] for the short history. It is instructive to stress, that the construction of q-deformation originates in the theory of the quantum integrable models and conformal field theory [see Faddeev [2]]. In this lecture I plan to survey some new developments on a representative example of the rang 1 SL(2) case.

Keywords

Hopf Algebra Quantum Group Real Structure Spectral Problem Conformal Block 
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.

Notes

Acknowledgements

This work was partially supported by RFBR grants 11-01-00570a and 11-01-12037ofi-m and the programm “Mathematical problems of nonlinear dynamics” of Russian Academy of Sciences.

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.St. Petersburg Department of Steklov Mathematical Institute, St. PetersburgRussia St. Petersburg State UniversitySt. PetersburgRussia

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