Unified quantization of three-dimensional bialgebras
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 17, Tome 291 (2002), pp. 169-184
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{ZNSL_2002_291_a9,
author = {E. V. Damaskinsky and P. P. Kulish and M. A. Sokolov},
title = {Unified quantization of three-dimensional bialgebras},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {169--184},
publisher = {mathdoc},
volume = {291},
year = {2002},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_291_a9/}
}
TY - JOUR AU - E. V. Damaskinsky AU - P. P. Kulish AU - M. A. Sokolov TI - Unified quantization of three-dimensional bialgebras JO - Zapiski Nauchnykh Seminarov POMI PY - 2002 SP - 169 EP - 184 VL - 291 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2002_291_a9/ LA - ru ID - ZNSL_2002_291_a9 ER -
E. V. Damaskinsky; P. P. Kulish; M. A. Sokolov. Unified quantization of three-dimensional bialgebras. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 17, Tome 291 (2002), pp. 169-184. http://geodesic.mathdoc.fr/item/ZNSL_2002_291_a9/