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On Benkart-Zelmanov intersetion matrix Lie algebras

Xu Mang

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Abstract

Benkart and Zelmanov defined one kind of intersetion matrix Lie algebras for the multi-affinzation cases when they studied the structure and classfication of the Lie algebras graded by non simplylaced finite root systems.In this note it is showed that every intersetion matrix Lie algebra defined by them is actually isomorphic to the corresponding complex semi-simple Lie algebra.

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Benkart and Zelmanov defined one kind of intersetion matrix Lie algebras for the multi-affinzation cases when they studied the structure and classfication of the Lie algebras graded by non simplylaced finite root systems.In this note it is showed that every intersetion matrix Lie algebra defined by them is actually isomorphic to the corresponding complex semi-simple Lie algebra.

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Available abstract

Benkart and Zelmanov defined one kind of intersetion matrix Lie algebras for the multi-affinzation cases when they studied the structure and classfication of the Lie algebras graded by non simplylaced finite root systems.In this note it is showed that every intersetion matrix Lie algebra defined by them is actually isomorphic to the corresponding complex semi-simple Lie algebra.

Key concepts: Lie conformal algebra, Mathematics, Adjoint representation of a Lie algebra, Lie algebra, Graded Lie algebra, Affine Lie algebra, Killing form, Pure mathematics

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