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Universal R-matrices for generalized Jordanian r-matrices

Title:

Universal R-matrices for generalized Jordanian r-matrices

Samsonov, Maxim (2004) Universal R-matrices for generalized Jordanian r-matrices. PhD thesis, Concordia University.

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Abstract

Quantization of classical integrable models by the Quantum Inverse Scattering Method requires transition from classical r -matrices to the quantum ones. The twists are the special elements in the algebra of observables, which help to build new classical and quantum r -matrices. In this thesis we develop an approach to explicit derivation of quasiclassical twists for higher dimensional analogs of Jordanian r -matrices. The twists are obtained as limits of more general quantum twists which allow a simple description. The considered class of r -matrices includes the skew-symmetric Cremmer-Gervais r -matrices as well as the extended Jordanian ones. The quantum analogs for both twists are obtained.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (PhD)
Authors:Samsonov, Maxim
Pagination:iii, 64 leaves ; 29 cm.
Institution:Concordia University
Degree Name:Ph. D.
Program:Mathematics and Statistics
Date:2004
Thesis Supervisor(s):Korotkin, D
ID Code:7994
Deposited By:Concordia University Libraries
Deposited On:18 Aug 2011 14:12
Last Modified:18 Aug 2011 14:12
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