基于简单序列确定复数域上的简单有限维 Lie 代数
数学物理
2025-10-23 v1 代数几何
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摘要
presented a novel method for determining which Dynkin diagrams represent simple finite-dimensional Lie algebras over . It is based on a condition that is both necessary and sufficient for a suitably defined Cartan matrix to be expressible by scalar products in a Euclidean vector space. The sufficiency of this condition makes unnecessary subsequent verification of the existence of a Lie algebra or root system corresponding to each Dynkin diagram by explicit construction. The Dynkin diagrams are selected by examination of an easily calculated sequence of minors of a symmetrised Cartan matrix. These minors are mostly integers.
引用
@article{arxiv.2510.19703,
title = {Identifying the simple finite-dimensional Lie algebras over $\mathbb{C}$ by means of simple sequences},
author = {Kai Neergård},
journal= {arXiv preprint arXiv:2510.19703},
year = {2025}
}