Leibniz algebras defined by tensor product of Lie algebras

YAN Qian-qian

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Nov. 2011

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YAN Qian-qian. Leibniz algebras defined by tensor product of Lie algebras[J]. Journal of East China Normal University (Natural Sciences), 2011, (5): 93-102.

Citation:

YAN Qian-qian. Leibniz algebras defined by tensor product of Lie algebras[J]. Journal of East China Normal University (Natural Sciences), 2011, (5): 93-102.

YAN Qian-qian. Leibniz algebras defined by tensor product of Lie algebras[J]. Journal of East China Normal University (Natural Sciences), 2011, (5): 93-102.

Citation:

YAN Qian-qian. Leibniz algebras defined by tensor product of Lie algebras[J]. Journal of East China Normal University (Natural Sciences), 2011, (5): 93-102.

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Leibniz algebras defined by tensor product of Lie algebras

YAN Qian-qian

1.
Department of Mathematics, East China Normal University, Shanghai 200241, China

Received Date: 2011-02-01
Rev Recd Date: 2011-05-01
Publish Date: 2011-09-25

Abstract

Abstract

By the definition of $\mathrm{Leibniz}$ algebra, we showed that \ $\mathcal{G}\otimes\mathcal{G}$\ was a $\mathrm{Leibniz}$\ algebra when \ $\mathcal{G}$\ was a $ \mathrm{Lie}$ algebra. We also proved that $\mathcal{G}\otimes\mathcal{G}$\ and $\mathcal{G}$\ have the same dimension of invariant symmetric bilinear forms in a special case, and the dimension of the derivation algebra of\ $\mathcal{G}$\ is always less than that of $\mathcal{G}\otimes\mathcal{G}$. $\mathcal{G}\boxtimes\mathcal{G}$\ is one of the important \ $\mathrm{Lie}$\ algebra induced by $\mathcal{G}\otimes\mathcal{G}$, and $\mathcal{G}\boxtimes\mathcal{G}$\ is isomorphic to $\mathcal{G}$\ when $\mathcal{G}$\ is a finite dimensional semi-simple\ $\mathrm{Lie}$\ algebra.
- Leibniz algebra,
- invariant symmetric bilinear form,
- tensor product,
- derivation,

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References(1)

References

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