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.