LEFT-INVARIANT CONFORMAL VECTOR FIELDS ON NON-SOLVABLE LIE GROUPS

被引：4
|
作者：
Zhang, Hui [1 ,2 ]
Chen, Zhiqi [1 ,2 ]
Tan, Ju [3 ]
机构：
[1] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China
[2] Nankai Univ, LPMC, Tianjin 300071, Peoples R China
[3] Anhui Univ Technol, Sch Math & Phys, Maanshan 243032, Peoples R China
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Conformal vector fields; pseudo-Riemannian Lie groups; solvable Lie groups;
D O I：
10.1090/proc/15272
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let (G, <., .>) be a pseudo-Riemannian Lie group of type (p, q) with the Lie algebra g. In this paper, we prove that G is solvable if (G, <., .>) admits a non-Killing left-invariant conformal vector field and dim[g, g] = dimg-min(p, q) + 1 for min(p, q) >= 2. Then we construct a non-solvable pseudo-Riemannian Lie group G of type (p, q) which admits a non-Killing left-invariant conformal vector field and dim[g, g] = dimg - min(p, q)+ d for any p, q >= 3 and 2 <= d <= min(p, q) - 1. It gives a negative answer to a forthcoming conjecture by H. Zhang and Z. Chen.
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页码：843 / 849
页数：7
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