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Zapiski Nauchnykh Seminarov POMI, 2002, Volume 291, Pages 169–184
(Mi znsl1656)
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This article is cited in 1 scientific paper (total in 2 paper)
Unified quantization of three-dimensional bialgebras
E. V. Damaskinskya, P. P. Kulishb, M. A. Sokolovc a Military Technical University
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
c St. Petersburg Institute of Machinery
Abstract:
The joint multiparameter quantization of several three-dimensional Lie algebras is given. Among the quantized algebras one finds the Heisenberg algebra, the algebra of motions of the (pseudo)euclidean plane and $su(2)$. Such a quantization is possible because all of the mentioned algebras are dual to the same solvable Lie algebra.
The explicit form of the number $R$-matrix is given which allows to encode some of the commutation relations in the form of the RTT-equation.
Received: 27.09.2002
Citation:
E. V. Damaskinsky, P. P. Kulish, M. A. Sokolov, “Unified quantization of three-dimensional bialgebras”, Questions of quantum field theory and statistical physics. Part 17, Zap. Nauchn. Sem. POMI, 291, POMI, St. Petersburg, 2002, 169–184; J. Math. Sci. (N. Y.), 125:2 (2005), 193–202
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https://www.mathnet.ru/eng/znsl1656 https://www.mathnet.ru/eng/znsl/v291/p169
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