Chains of twists for classical Lie algebras

Abstract

For chains of regular injections A_p -> A_(p-1) -> ... -> A_1 -> A_0 of Hopf algebras the sets of maximal extended Jordanian twists F_E are considered. We prove that under certain conditions there exists for A_0 the twist composed by the factors (F_E)_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_F(g) are explicitly demonstrated for the case of g = so(9).