Parabolic twists for the linear algebras A n−1

Abstract

New solutions of twist equations for the universal enveloping algebras U (An−1) are found. These solutions can be represented as products of full chains of extended Jordanian twists \( \mathcal{F}_{\widehat{ch}} \) Abelian factors (“rotations”) \( \mathcal{F}^R \), and sets of quasi-Jordanian twists \( \mathcal{F}^{\widehat{J}} \). The latter are generalizations of Jordanian twists (with carrier b2) for special deformed extensions of the Hopf algebra U (b2). The carrier subalgebra \( g_\mathcal{P} \) for the composition \( \mathcal{F}_\mathcal{P} = \mathcal{F}^{\widehat{J}} \mathcal{F}^R \mathcal{F}_{\widehat{ch}} \) is a nonminimal parabolic subalgebra in A n−1 such that \( g_\mathcal{P} \cap \mathbb{N}_g^ - \ne \emptyset \). The parabolic twisting elements \( \mathcal{F}_\mathcal{P} \) are obtained in an explicit form. Details of the construction are illustrated by considering the examples n = 4 and n = 11. Bibliography: 21 titles.