Multiparametric quantum gl(2): Lie bialgebras, quantum R-matrices and non-relativistic limits
Angel Ballesteros, Francisco J. Herranz, Preeti Parashar
Abstract
Multiparametric quantum deformations of gl(2) are studied through a complete classification of gl(2) Lie bialgebra structures. From them, the non-relativistic limit leading to harmonic oscillator Lie bialgebras is implemented by means of a contraction procedure. New quantum deformations of gl(2) together with their associated quantum R-matrices are obtained and other known quantizations are recovered and classified. Several connections with integrable models are outlined.
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