Quantum duality in quantum deformations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Quantum duality in quantum deformations

Authors:	V D Lyakhovsky

Institution:	(1) St. Petersburg State University, St. Petersburg, Russia

Abstract:	In accordance with the quantum duality principle, the twisted algebra $U_\mathcal{F} (\mathfrak{g})$ is equivalent to the quantum group $Fun_{def} (\mathfrak{G}^\# )$ and has two preferred bases: one inherited from the universal enveloping algebra $U(\mathfrak{g})$ and the other generated by coordinate functions of the dual Lie group $\mathfrak{G}^\#$ . We show howthe transformation $\mathfrak{g} \to \mathfrak{g}^\#$ can be explicitly obtained for any simple Lie algebra and a factorable chain $\mathcal{F}$ of extended Jordanian twists. In the algebra $\mathfrak{g}^\#$ , we introduce a natural vector grading $\Gamma (\mathfrak{g}^\# )$ , compatible with the adjoint representation of the algebra. Passing to the dual-group coordinates allows essentially simplifying the costructure of the deformed Hopf algebra $U_\mathcal{F} (\mathfrak{g})$ , considered as a quantum group $Fun_{def} (\mathfrak{G}^\# )$ . The transformation $\mathfrak{g} \to \mathfrak{g}^\#$ can be used to construct new solutions of the twist equations. We construct a parameterized family of extended Jordanian deformations $U_{\varepsilon \mathcal{J}} (\mathfrak{s}\mathfrak{l}(3))$ and study it in terms of $\mathcal{S}\mathcal{L}(3)^\#$ ; we find new realizations of the parabolic twist. Dedicated to the birthday of my teacher, Yurii Novozhilov __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 1, pp. 112–125, July, 2006.

Keywords:	Lie— Poisson structures quantum deformations of symmetry quantum duality
本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏