多重loop李（超）代数是无限维李理论中的一类重要研究对象。近期的研究表明每个有扭多重loop李（超）代数都是一个无扭多重loop李（超）代数关于多变量Laurent多项式环的一个Galois扩张的扭形式。这些扭形式可由相应的非交换Galois上同调集分类。这一事实使得非交换Galois上同调方法进入到无限维李理论的研究中。..本项目拟利用非交换Galois上同调方法对有扭多重loop李代数整基的构造、有扭多重loop李代数的表示和有扭多重loop李超代数的分类等三方面的问题进行研究。预期可通过对这些具体问题的研究获得扩张仿射李代数的相关结果。

Multiloop Lie (super)algebras are important objects in infinite dimensional Lie theory. Recent investigations show that every twisted multiloop Lie (super)algebra is a twisted form of an untwisted multiloop Lie (super)algebra with respect to a Galois extension of certain multivariable Laurent polynomial ring. These twisted forms can be classified by the corresponding non-abelian Galois cohomology set. This fact introduced non-abelian Galois cohomology methods into the study of infinite-dimensional Lie theory..With the use of non-abelian Galois cohomology methods, this project plans to study problems concerning the construction of integral bases of twisted multiloop Lie algebras, the representations of twisted multiloop Lie algebras and the classifications of twisted multiloop Lie superalgebras. These researches are expected to yield a few related results on extended affine Lie algebras.