论文标题
$ w $ - 代数通过LAX类型操作员
$W$-algebras via Lax type operators
论文作者
论文摘要
$ w $ - 代数是与有限的尺寸Lie代数$ \ Mathfrak G $和通过汉密尔顿减少的nilpotent元素$ f $相关的代数结构。在本说明中，我们对基于LAX类型操作员概念的（经典仿射和量子有限）的研究（经典仿射和量子有限）的研究进行了回顾。对于$ \ mathfrak g $的有限维表示，使用通用的准扣理论构建了$ w $ algebras的lax类型运算符。该操作员携带有关$ W $ - 代数的结构和属性的几片信息，并显示了$ W $ - 代数与Yangians和可LAX类型方程式的Hamiltonian层次结构的深厚联系。
$W$-algebras are certain algebraic structures associated to a finite dimensional Lie algebra $\mathfrak g$ and a nilpotent element $f$ via Hamiltonian reduction. In this note we give a review of a recent approach to the study of (classical affine and quantum finite) $W$-algebras based on the notion of Lax type operators. For a finite dimensional representation of $\mathfrak g$ a Lax type operator for $W$-algebras is constructed using the theory of generalized quasideterminants. This operator carries several pieces of information about the structure and properties of the $W$-algebras and shows the deep connection of the theory of $W$-algebras with Yangians and integrable Hamiltonian hierarchies of Lax type equations.
