Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras

Details Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras

1994-12-09

arxiv.org/abs/hep-th/9412083v3

J.Math.Phys. 36 (1995) 5916-5937

Physics

High Energy Physics

High Energy Physics - Theory

26 pages LATEX

Scientific paper

10.1063/1.531368

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, Poincar\'e and Galilean algebras.

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