In this article, we are interested in some subspaces of the exterior algebra of a simple Lie algebra \(\mathfrak {g}\). In particular, we prove that some graded subspaces of degree d generate the \({\mathfrak {g}}\)-module \(\bigwedge ^{d}{\mathfrak {g}}\) for some integers d.

中文翻译：

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简单李代数外代数的一些子空间

在本文中，我们对简单李代数\（\ mathfrak {g} \）的外部代数的某些子空间感兴趣。特别是，我们证明了某些等级d的渐变子空间会为某些整数d生成\（{\ mathfrak {g}} \）-模块\（\ bigwedge ^ {d} {\ mathfrak {g}} \}。