Multiparametric quantum gl(2): Lie bialgebras, quantum R-matrices and non-relativistic limits

Angel Ballesteros; Francisco J. Herranz; Preeti Parashar

arxiv: math/9806149 · v2 · submitted 1998-06-26 · 🧮 math.QA · hep-th

Multiparametric quantum gl(2): Lie bialgebras, quantum R-matrices and non-relativistic limits

Angel Ballesteros , Francisco J. Herranz , Preeti Parashar This is my paper

classification 🧮 math.QA hep-th

keywords quantumbialgebrasdeformationsmultiparametricnon-relativisticassociatedbialgebraclassification

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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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