Some remarks on semisimple Leibniz algebras

JOURNAL OF ALGEBRA

卷:410

Article

Gomez-Vidal, S.¹  Khudoyberdiyev, A. Kh.²  Omirov, B. A.² 

[1] Univ Seville, Dept Matemat Aplicada 1, E-41012 Seville, Spain

[2] Acad Uzbekistan, Inst Math & Informat Technol, Tashkent 100125, Uzbekistan

关键词: Lie algebras;    Leibniz algebras;    Simplicity;    Semisimplicity;    Solvable radical;    Levi's Theorem;   

DOI  :  10.1016/j.jalgebra.2013.04.027

来源: Elsevier

【 摘 要 】

From Levi's Theorem it is known that every finite-dimensional Lie algebra over a field of characteristic zero is decomposed into semidirect sum of its solvable radical and semisimple subalgebra. Moreover, semisimple part is the direct sum of simple ideals. In Barnes (preprint) [6] Levi's Theorem is extended to the case of Leibniz algebras. In the present paper we investigate the semisimple Leibniz algebras and we show that the splitting theorem for semisimple Leibniz algebras is not true. Moreover, we consider some special classes of the semisimple Leibniz algebras and we find a condition under which they decompose into direct sum of simple ideals. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free