On Z-gradations of twisted loop Lie algebras of complex simple Lie algebras

Abstract

We define the twisted loop Lie algebra of a finite dimensional Lie algebra $\mathfrak{g}$ as the Fréchet space of all twisted periodic smooth mappings from $\mathbb{R}$ to $\mathfrak{g}$. Here the Lie algebra operation is continuous. We call such Lie algebras Fréchet Lie algebras. We introduce the notion of an integrable $\mathbb{Z}$-gradation of a Fréchet Lie algebra, and find all inequivalent integrable $\mathbb{Z}$-gradations with finite dimensional grading subspaces of twisted loop Lie algebras of complex simple Lie algebras.

26 pages

References in corpus (3)

• Multidimensional Toda type systems
• Nonabelian Toda equations associated with classical Lie groups
• On classification of non-abelian Toda systems

Cited by in corpus (6)

• Toda equations associated with loop groups of complex classical Lie groups
• The rational dressing for abelian twisted loop Toda systems
• Abelian Toda solitons revisited
• On Z-graded loop Lie algebras, loop groups, and Toda equations
• More non-Abelian loop Toda solitons
• Solving non-abelian loop Toda equations