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Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras

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arxiv hep-th/9412083 v3 pith:XEIJOCW5 submitted 1994-12-09 hep-th math.QAq-alg

Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras

A. Ballesteros , N.A. Gromov , F.J. Herranz , M.A. del Olmo , M. Santander This is my paper
classification hep-th math.QAq-alg
keywords algebrasbialgebracontractionsdeformationsexplicitlyquantumquasi-orthogonalalgebra
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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, Poincar\'e and Galilean algebras.

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