Restricted Lie algebras all whose elements are semisimple

doi:10.1007/s11464-010-0091-8

Front Math Chin

2011, Vol. 6

Issue (1) : 61-70 https://doi.org/10.1007/s11464-010-0091-8

RESEARCH ARTICLE

Restricted Lie algebras all whose elements are semisimple

Liangyun CHEN¹, Xiaoning XU²(

), Yongzheng ZHANG¹

1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China; 2. School of Mathematics, Liaoning University, Shenyang 110036, China

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Abstract

People studied the properties and structures of restricted Lie algebras all whose elements are semisimple. It is the main objective of this paper to continue the investigation in order to obtain deeper structure theorems. We obtain some sufficient conditions for the commutativity of restricted Lie algebras, generalize some results of R. Farnsteiner and characterize some properties of a finite-dimensional semisimple restricted Lie algebra all whose elements are semisimple. Moreover, we show that a centralsimple restricted Lie algebra all whose elements are semisimple over a field of characteristic p>7 is a form of a classical Lie algebra.

Keywords Restricted Lie algebra ad-semisimple simple-semiabelian semisimple element p-simple-semiabelian

Corresponding Author(s): XU Xiaoning,Email:ldxxn@yahoo.com.cn

Issue Date: 01 February 2011

Cite this article:

Liangyun CHEN,Xiaoning XU,Yongzheng ZHANG. Restricted Lie algebras all whose elements are semisimple[J]. Front Math Chin, 2011, 6(1): 61-70.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-010-0091-8
https://academic.hep.com.cn/fmc/EN/Y2011/V6/I1/61

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