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2011•Journal of Nonlinear Mathematical PhysicsOpen access

Derivations of the 3-Lie Algebra Realized by gl(n, ℂ)

Ruipu Bai, Jinxiu Wang, Zhenheng Li

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Abstract

This paper studies structures of the 3-Lie algebra M realized by the general linear Lie algebra gl(n, ℂ). We show that M has only one nonzero proper ideal. We then give explicit expressions of both derivations and inner derivations of M. Finally, we investigate substructures of the (inner) derivation algebra of M.

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This paper studies structures of the 3-Lie algebra M realized by the general linear Lie algebra gl(n, ℂ). We show that M has only one nonzero proper ideal. We then give explicit expressions of both derivations and inner derivations of M. Finally, we investigate substructures of the (inner) derivation algebra of M.

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Available abstract

This paper studies structures of the 3-Lie algebra M realized by the general linear Lie algebra gl(n, ℂ). We show that M has only one nonzero proper ideal. We then give explicit expressions of both derivations and inner derivations of M. Finally, we investigate substructures of the (inner) derivation algebra of M.

Key concepts: Mathematics, Graded Lie algebra, Algebra over a field, Ideal (ethics), Lie algebra, Lie superalgebra, Pure mathematics, Universal enveloping algebra

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