Frontiers of Mathematics in China >
Restricted Lie algebras all whose elements are semisimple
Received date: 21 Jun 2010
Accepted date: 12 Oct 2010
Published date: 01 Feb 2011
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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.
Liangyun CHEN , Xiaoning XU , Yongzheng ZHANG . Restricted Lie algebras all whose elements are semisimple[J]. Frontiers of Mathematics in China, 2011 , 6(1) : 61 -70 . DOI: 10.1007/s11464-010-0091-8
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