The Hom-Yang-Baxter equation and Hom-Lie algebras
The Hom-Yang-Baxter equation and Hom-Lie algebras
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DOI：
10.1063/1.3571970
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发表时间：
2009-05
期刊：
影响因子：
--
通讯作者：
Donald Yau
中科院分区：
文献类型：
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作者：
Donald Yau
受Hom-Lie代数研究的启发，作者在早期的论文中引入了一个扭曲的Yang-巴克斯特方程，称为Hom-Yang-巴克斯特方程（HYBE）。本文构造了HYBE的多类解。HYBE的某些解与sl（2）的量子包络代数、Jones-Conway多项式和Yetter-Drinfel'd模密切相关。我们还从给定的HYBE解构造了一个新的无限序列。沿着这条路，我们计算了（1+1）-Poincare代数和sl（2）上的所有李代数自同态。
Motivated by recent work on Hom-Lie algebras, a twisted version of the Yang-Baxter equation, called the Hom-Yang-Baxter equation (HYBE), was introduced by the author in an earlier paper. In this paper, several more classes of solutions of the HYBE are constructed. Some of these solutions of the HYBE are closely related to the quantum enveloping algebra of sl(2), the Jones-Conway polynomial, and Yetter-Drinfel'd modules. We also construct a new infinite sequence of solutions of the HYBE from a given one. Along the way, we compute all the Lie algebra endomorphisms on the (1+1)-Poincare algebra and sl(2).