Quantum Lie algebras of type A_n positive, PBW bases and the Yang-Baxter equation

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We show explicitly a generalised Lie algebra embedded in the positive and negative parts of the Drinfeld-Jimbo quantum groups of type A_n. Such a generalised Lie algebra satisfy axioms closely related to the ones found by S.L. Woronowicz. For the universal enveloping algebra of such generalised Lie algebras we establish several conditions in order to obtain bases of type Poincaré-Birkhoff-Witt. Besides a graded algebra is proposed and some relations with the quantum Yang-Baxter equation are studied.
9 pages, AMSLaTeX 1.2, no figures

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Quantum Algebra, 17B70 (Primary) 17B37, 17B35 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/77203

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9807140
 http://arxiv.org/abs/math/9807140

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arXiv