Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras
نویسندگان
چکیده
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 Uzso(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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