Chains of twists for classical Lie algebras
P. P. Kulish, V. D. Lyakhovsky, M. A. del Olmo
Abstract
For chains of regular injections Ap -> A(p-1) -> ... -> A1 -> A0 of Hopf algebras the sets of maximal extended Jordanian twists FE are considered. We prove that under certain conditions there exists for A0 the twist composed by the factors (FE)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 An, Bn and Dn. The properties of the deformation produced by a chain UF(g) are explicitly demonstrated for the case of g = so(9).
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