LIE BIALGEBRA CONTRACTIONS AND QUANTUM DEFORMATIONS OF QUASI-ORTHOGONAL ALGEBRAS

Lie bialgebra contractions are introduced and classified. A non-degene rate co-boundary bialgebra structure is implemented into all pseudo-or thogonal 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 cons truction is explicitly given for N=2,3,4. All Lie bialgebra contractio ns studied in this paper define Hopf algebra contractions for the Drin fel'd-Jimbo deformations U(z)so(p,q). They are explicitly used to gene rate new non-semisimple quantum algebras as it is the case for the Euc lidean, Poincare, and Galilean algebras. (C) 1995 American Institute o f Physics.