Chains of twists for classical Lie algebras

For chains of regular injections A(p) subset of A(p-1) subset of ... subset of A(1) subset of A(0) of Hopf algebras the sets of maximal extended Jordanian twists {F-epsilon k}are considered. We prove that under certain conditions there exists for A(0) the twist F-beta k<0 composed of the factors F-epsilon k,. The general construction of a chain of twists is applied to the universal envelopings U (g) of classical Lie algebras g. We study the chains for the infinite series A(n), B-n and D-n. The properties of the deformation produced by a chain U(g)F-beta k<0 are explicitly demonstrated for the case of g = so(9).