Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras

Lie bialgebra contractions are introduced and classified. A non-degenerate coboundary bialgebra structure is implemented into all pseudo-orthogonal real algebras so(p,q) starting from the one corresponding to so(N+1). It allows us to introduce a set of Lie bialgebra contractions which leads to Lie bialgebras of quasi-orthogonal algebras. This construction is explicitly given for 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.