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2013, № 9 (158)



Mescherina E.V., Pikhtilkov S.A. ON SOME PROPETIES OF LIE ALGEBRAS INNER IDEALSThe concept of the inner ideal Benkart Georgia was introduced. F. Lopez, E. Garcia, G. Lozano investigated the notion of inner ideal with respect to the Artinian Jordan pairs with. In this paper we study some properties of inner ideals. It is also considered the definition of Artinian in three senses and communication between them. Artinian special Lie algebras was considered earlier by Y.A. Bahturin, S.A. Pikhtilkov, and V.M. Polyakov.Key words: Lie algebra, inner ideal, Artinian.

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References:

1. Benkart, G. On inner ideals and ad-nilpotent elements of Lie algebras / G. Benkart// Transaction of the American Mathematical Society.– 1977.– V. 232.– P. 61-81.

2. Fernandez Lopez A. An Artinian theory for Lie algebras /Fernandez Lopez A., Garcia E., Gomez Lozano M.// Journal of Algebra.– 2008.– V. 319.– P. 938-951.

3. Bahturin, Y.A. Artinian special Lie algebras / / Y.A. Bahturin / Algebra: Collection of scientific papers/ M.: MSU, 1982. — P. 24-26.

4. Pikhtilkov, S.A. Artinian special Lie algebras / S.A. Pikhtilkov / / Algorithmic problems in group theory and semigroups: Collection of scientific papers / Tula: TSPU the name of L.N. Tolstoy, 2001. — P. 189-194.

5. Pikhtilkov, S.A. On locally nilpotent Artinian Lie algebras / S.A. Pikhtilkov, V.M. Polyakov / / Chebyshev collection. — 2005. — T. 6. — V. 1. — P. 163-169.

6. Pikhtilkov, S.A. Structural theory of special Lie algebras / S.A. Pikhtilkov. — Tula: TSPU the name of L.N. Tolstoy, 2005. — P. 45-48.


About this article

Authors: Meshcherina E.V., Pihtilkov S.A.

Year: 2013


Editor-in-chief
Sergey Aleksandrovich
MIROSHNIKOV

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