关于三维复 hom-Lie 代数的分类
环与代数
2019-11-06 v2 量子代数
表示论
摘要
我们在同构意义下对三维复 Lie 代数上具有幂零扭曲映射的 hom-Lie 结构进行分类，并对此类族中的所有退化进行分类。此处提出的思路与技术可轻易推广以研究其他代数结构中的类似问题，并提供不同视角，由此可攻克刚 Lie 代数中令人关注的经典开放问题。
引用
@article{arxiv.1910.13528,
title = {On the classification of $3$-dimensional complex hom-Lie algebras},
author = {Edison Alberto Fernández-Culma and Nadina Elizabeth Rojas},
journal= {arXiv preprint arXiv:1910.13528},
year = {2019}
}
备注
43 pages and a companion file providing a detailed, step-by-step, explanation of our results. In the previous version, we made a mistaked by affirming that the Theorem4.3 in Ongong'a, Richter, Silvestrov "Classification of 3-dim. Hom-Lie algebras" is wrong. Our error was due to that we didn't note the condition $C_{1,3}^2\neq 0$ to define the family $H_{6}^3$. Please accept our sincere apoogies