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, Poincare, and Galilean algebras.