经典仿射与经典仿射分式W-代数的结构
Structure of classical affine and classical affine fractional W-algebras
摘要：
我们证明了通过一个经典的BRST复形可以构造一个经典的仿射W-代数。这个定义阐明了经典仿射W-代数可以看作量子仿射W-代数的准经典极限。给出了经典仿射分式W-代数作为Poisson顶点代数的定义。与经典仿射情形一样，经典仿射分式W-代数有两个相容的$λ$ -括号，并且同构于微分多项式代数作为微分代数。当一个经典的仿射分数W-代数与一个极小幂零元相关联时，我们给出了自由生成元的显式形式，并计算了它们之间的$λ$ -括号。在对经典的仿射分数W-代数作一定假设的条件下，利用广义Drinfel'd和Sokolov约化，得到了与该代数相关的可积系统的无穷序列.
英文摘要：
We show that one can construct a classical affine W-algebra via a classical BRST complex. This definition clarifies that classical affine W-algebras can be considered as quasi-classical limits of quantum affine W-algebras. We also give a definition of a classical affine fractional W-algebra as a Poisson vertex algebra. As in the classical affine case, a classical affine fractional W-algebra has two compatible $λ$-brackets and is isomorphic to an algebra of differential polynomials as a differential algebra. When a classical affine fractional W-algebra is associated to a minimal nilpotent, we describe explicit forms of free generators and compute $λ$-brackets between them. Provided some assumptions on a classical affine fractional W-algebra, we find an infinite sequence of integrable systems related to the algebra, using the generalized Drinfel'd and Sokolov reduction.
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