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Zapiski Nauchnykh Seminarov POMI, 2002, Volume 291, Pages 169–184 (Mi znsl1656)  
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
Full-text PDF (192 kB) Citations (2)
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
English version:
Journal of Mathematical Sciences (New York), 2005, Volume 125, Issue 2, Pages 193–202
DOI: https://doi.org/10.1023/B:JOTH.0000049571.26334.b7
Bibliographic databases:
UDC: 517.9
Language: Russian
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
Citation in format AMSBIB
\Bibitem{DamKulSok02}
\by E.~V.~Damaskinsky, P.~P.~Kulish, M.~A.~Sokolov
\paper Unified quantization of three-dimensional bialgebras
\inbook Questions of quantum field theory and statistical physics. Part~17
\serial Zap. Nauchn. Sem. POMI
\yr 2002
\vol 291
\pages 169--184
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1656}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1948815}
\zmath{https://zbmath.org/?q=an:1095.17005}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 125
\issue 2
\pages 193--202
\crossref{https://doi.org/10.1023/B:JOTH.0000049571.26334.b7}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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