We define the twisted loop Lie algebra of a finite dimensional Lie algebra$\mathfrak g$ as the Fr\'echet space of all twisted periodic smooth mappingsfrom $\mathbb R$ to $\mathfrak g$. Here the Lie algebra operation iscontinuous. We call such Lie algebras Fr\'echet Lie algebras. We introduce thenotion of an integrable $\mathbb Z$-gradation of a Fr\'echet Lie algebra, andfind all inequivalent integrable $\mathbb Z$-gradations with finite dimensionalgrading subspaces of twisted loop Lie algebras of complex simple Lie algebras.
展开▼
机译：我们将有限维李代数$ \ mathfrak g $的扭曲环李代数定义为所有从$ \ mathbb R $到$ \ mathfrak g $的扭曲周期光滑映射的Fr'echet空间。李代数运算在这里是连续的。我们称这类李代数为Fr'echet李代数。我们介绍了Fr'echet Lie代数的可积$ \ mathbb Z $阶跃的概念，并通过复杂的简单Lie代数的扭曲环Lie代数的有限维分级子空间，找到了所有不等价的$ \ mathbb Z $阶跃。
展开▼
