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On the relationship between the class of a Lie algebra and the classes of its subalgebras.

机译：李代数的类与其子代类的关系。

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A classical nilpotency result considers finite p-groups whose proper subgroups all have class bounded by a fixed number n . We consider the analogous property in nilpotent Lie algebras. In particular, we investigate whether this condition puts a bound on the class of the Lie algebra. Some p-group results and proofs carry over directly to the Lie algebra case, some carry over with modified proofs and some fail. For the final of these cases, a certain metabelian Lie algebra is constructed to show a case when the p-groups and Lie algebra cases differ.

机译：一个经典的幂等结果考虑了有限的p组，它们的适当子组都具有以固定数n为边界的类。我们考虑了幂立李代数中的类似性质。特别是，我们研究了这种条件是否对李代数的类设置了限制。一些p-group的结果和证明直接延续到李代数的情况，一些继续进行修改的证明而有些失败。对于这些情况中的最后一个，构造了一个变态李代数，以显示p组和李代数情况不同的情况。

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作者
Suanmali, Suthathip.;
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作者单位

North Carolina State University.;

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授予单位 North Carolina State University.;
学科 Mathematics.
学位 Ph.D.
年度 2007
页码 42 p.
总页数 42
原文格式 PDF
正文语种 eng
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专利

1. On the relationship between the class of a lie algebra and the classes of its subalgebras [J] . Suanmali S International journal of algebra and computation . 2008,第1期

机译：谎言代数的类与其子代数的类之间的关系
2. ALGEBRAIC GEOMETRY OVER FREE METABELIAN LIE ALGEBRAS. Ⅰ. U-ALGEBRAS AND UNIVERSAL CLASSES [J] . E. Yu. Daniyarova, I. V. Kazatchkov, V. N. Remeslennikov Journal of Mathematical Sciences . 2006,第5期

机译：自由Metalbelian Lie代数上的代数几何。 Ⅰ。 U-代数和通用类
3. The Koszul homomorphism for a pair of Lie algebras in the theory of exotic characteristic classes of Lie algebroids [J] . Bogdan Balcerzak, Jan Kubarski Topology and its applications . 2013,第12期

机译：李代数奇异特征类理论中一对李代数的Koszul同态
4. Rigidity of Some Classes of Lie Algebras in Connection to Leibniz Algebras [C] . Abdulafeez O. Abdulkareem, Isamiddin S. Rakhimov, Sharifah K. Said Husain National Symposium on Mathematical Sciences . 2014

机译：有关Leibniz代数的某些类别的谎言代数的僵硬
5. Nilpotent conjugacy classes of reductive p-adic Lie algebras and definability in Pas's language. [D] . Diwadkar, Jyotsna Mainkar. 2006

机译：还原p-adic Lie代数的幂次共轭类和Pas语言的可定义性。
6. CLASSIFICATION OF THE REAL INFINITE SIMPLE AND REAL INFINITE PRIMITIVE LIE ALGEBRAS [O] . Steven Shnider 2016

机译：实无限简单和实无限原始李代数的分类
7. Maximal subalgebras of Lie algebras containing Engel subalgebras. [O] . Towers, David A. 2012

机译：包含Engel子代数的Lie代数的最大子代数。
8. Conjugacy Classes in Lie Algebras and Algebraic Groups [R] . Richardson, R. W. 1966

机译：李代数和代数群中的共轭类

On the relationship between the class of a Lie algebra and the classes of its subalgebras.

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