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

Angel Ballesteros·Francisco J. Herranz·Preeti Parashar
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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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Angel Ballesteros, Francisco J. Herranz, Preeti Parashar. 1999-02-03. Multiparametric quantum gl(2): Lie bialgebras, quantum R-matrices and non-relativistic limits. https://doi.org/10.1088/0305-4470%2F32%2F12%2F010

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