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arXiv · hep-th/9412083

Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras

A. Ballesteros·N. A. Gromov·F. J. Herranz·M. A. del Olmo·M. Santander
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Abstract

Lie bialgebra contractions are introduced and classified. A non-degenerate coboundary bialgebra structure is implemented into all pseudo-orthogonal algebras $so(p,q)$ starting from the one corresponding to $so(N+1)$. It allows to introduce a set of Lie bialgebra contractions which leads to Lie bialgebras of quasi-orthogonal algebras. This construction is explicitly given for the cases $N=2,3,4$. All Lie bialgebra contractions studied in this paper define Hopf algebra contractions for the Drinfel'd-Jimbo deformations $U_z so(p,q)$. They are explicitly used to generate new non-semisimple quantum algebras as it is the case for the Euclidean, Poincaré and Galilean algebras.

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A. Ballesteros, N. A. Gromov, F. J. Herranz, M. A. del Olmo, M. Santander. 1994-12-12. Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras. https://doi.org/10.1063/1.531368

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