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On the Decompositions of Generalized Derivations of n-Lie Algebras

Zhao Guan-hua

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Abstract

The derivations which are special linear transformations play an important role in studying the construction and representation theory of n-Lie algebras.For further discussing the construction of n-Lie algebras , we introduce the generalized derivations of n-Lie algebras and show that they respectively form a Lie algebra. We also obtain the decompositions of several kinds of generalixed derivations respectively according to the decompositions of n-Lie algebras.

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The derivations which are special linear transformations play an important role in studying the construction and representation theory of n-Lie algebras.For further discussing the construction of n-Lie algebras , we introduce the generalized derivations of n-Lie algebras and show that they respectively form a Lie algebra. We also obtain the decompositions of several kinds of generalixed derivations respectively according to the decompositions of n-Lie algebras.

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Available abstract

The derivations which are special linear transformations play an important role in studying the construction and representation theory of n-Lie algebras.For further discussing the construction of n-Lie algebras , we introduce the generalized derivations of n-Lie algebras and show that they respectively form a Lie algebra. We also obtain the decompositions of several kinds of generalixed derivations respectively according to the decompositions of n-Lie algebras.

Key concepts: Mathematics, Lie algebra, Adjoint representation of a Lie algebra, Pure mathematics, Lie conformal algebra, Algebra over a field, Representation of a Lie group, Non-associative algebra

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