Lie Invariants in Two and Three Variables

• 作者: Jiaxiong Hu Murray R. Bremner
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 谎言 三变量 计算机代数 不变量 伴随表示 系数矩阵 李代数 发电机
• 年，卷（期）: 2014,（1）
• 页码范围: 95-116
• 页数: 22页
• 分类号: O141
• 语种: 中文

摘要

We use computer algebra to determine the Lie invariants of degree ≤ 12 in the free Lie algebra on two generators corresponding to the natural representation of the simple 3-dimensional Lie algebra sl2(C). We then consider the free Lie algebra on three generators, and compute the Lie invariants of degree ≤ 7 corresponding to the adjoint representation of sl2(C), and the Lie invariants of degree ≤ 9 corresponding to the natural representation of sl3(C). We represent the action of sl2(C) and sl3(C) on Lie polynomials by computing the coefficient matrix with respect to the basis of Hall words.