Construction of nice nilpotent Lie groups

被引：12
|
作者：
Conti, Diego [1 ]
Rossi, Federico A. [1 ]
机构：
[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via Cozzi 55, I-20125 Milan, Italy
来源：
JOURNAL OF ALGEBRA | 2019年 / 525卷
关键词：
Nilpotent Lie groups; Nice Lie algebras; NILMANIFOLDS; SOLITON; METRICS;
D O I：
10.1016/j.jalgebra.2019.01.020
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We illustrate an algorithm to classify nice nilpotent Lie algebras of dimension n up to a suitable notion of equivalence; applying the algorithm, we obtain complete listings for n <= 9. On every nilpotent Lie algebra of dimension <= 7, we determine the number of inequivalent nice bases, which can be 0, 1, or 2. We show that any nilpotent Lie algebra of dimension n has at most countably many inequivalent nice bases. (C) 2019 Elsevier Inc. All rights reserved.
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页码：311 / 340
页数：30
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