A new simple Lie algebra of characteristic three

Author:

Frank Marguerite

Abstract

We define a restricted simple algebra T T of dimension 18 over an arbitrary field of characteristic 3. From a certain property of its Cartan decomposition, we show T T to be nonisomorphic to any known algebra of identical dimension.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference6 articles.

1. Lie algebras of characteristic three with nondegenerate Killing form;Brown, Gordon;Trans. Amer. Math. Soc.,1969

2. Cartan subalgebras of the simple Lie 𝑝-algebras 𝑊_{𝑛} and 𝑆_{𝑛};Demuškin, S. P.;Sibirsk. Mat. \v{Z}.,1970

3. M. Frank, On a theory relating matric Lie algebras of characteristic 𝑝 and subalgebras of the Witt-Jacobson algebra, Progress Report I.T., Math. Dept., University of Minnesota, Minneapolis, Minn., 1943, pp. 107-121.

4. Classes of restricted Lie algebras of characteristic 𝑝. II;Jacobson, N.;Duke Math. J.,1943

5. Lie algebras of characteristic 𝑝;Kaplansky, Irving;Trans. Amer. Math. Soc.,1958

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Maximal tori of the Frank algebra;Journal of Mathematical Sciences;2012-07-29

2. Filtered deformations of lie algebras of the series R;Mathematical Notes;2012-04

3. Joins of ideals of subideals of Lie algebras;Archiv der Mathematik;1986-09

4. The classification problem for simple lie algebras of characteristic p;Algebra Carbondale 1980;1981

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