Quantization of Poisson pencils and generalized lie algebras |
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| Authors: | D. Gurevich V. Rubtsov |
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| Affiliation: | (1) Université de Valenciennes, 59304 Valenciennes, France;(2) Ecole Polytechnique, U.R.A. 169 du CNRS. Centre de Mathématiques, 91128 Palaiseau, France;(3) ITEP, Bol. Tcheremushkinskaya 25, 117259 Moscow, Russia |
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| Abstract: | We describe two types of Poisson pencils generated by a linear bracket and a quadratic one arising from a classical R-matrix. A quantization scheme is discussed for each. The quantum algebras are represented as the enveloping algebras of  generalized Lie algebras. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 3, pp. 476–488, June, 1995. |
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