Six-dimensional nilpotent Lie algebras

被引:88
作者
Cicalo, Serena [1 ]
de Graaf, Willem A. [2 ]
Schneider, Csaba [1 ]
机构
[1] Univ Lisbon, Ctr Algebra, P-1649003 Lisbon, Portugal
[2] Univ Trent, Dipartimento Matemat, I-38050 Povo, Trento, Italy
基金
匈牙利科学研究基金会;
关键词
Nilpotent Lie algebras; Six-dimensional Lie algebras; Second cohomology; Klein correspondence; Quadratic forms; Arf invariant; CLASSIFICATION; ORDER; PRIME;
D O I
10.1016/j.laa.2011.06.037
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We give a full classification of six-dimensional nilpotent Lie algebras over an arbitrary field, including fields that are not algebraically closed and fields of characteristic 2. To achieve the classification we use the action of the automorphism group on the second cohomology space, as isomorphism types of nilpotent Lie algebras correspond to orbits of subspaces under this action. In some cases, these orbits are determined using geometric invariants, such as the Gram determinant or the Arf invariant. As a byproduct, we completely determine, for a four-dimensional vector space V. the orbits of GL(V) on the set of two-dimensional subspaces of V boolean AND V. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码:163 / 189
页数:27
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