论文标题
（超对称）经典W- algebras的结构
Structures of (supersymmetric) classical W-algebras
论文作者
论文摘要
在本文的第一部分中，我们讨论了经典的W-Algebra $ \ Mathcal {w}（\ Mathfrak {g}，f），f）$与lie superalgebra $ \ mathfrak {g} $和nilpotent $ f $相关的lie superalgebra $ \ mathfrak和nilpotent $ f $。我们找到了$ \ Mathcal {W}（\ Mathfrak {g}，f）$的生成集，并计算它们之间的泊松支架。在第二部分是本文的主要部分，我们讨论了超对称的经典W-代数。我们介绍了两个不同的经典w-algebra $ \ mathcal {w}（\ Mathfrak {g}，f），f）$与lie superalgebra $ \ mathfrak {g} $相关的$ \ nilpotent元素$ f $ subalgebra isomorphic to $ \ \ mathak | 2 | 2 | 2 | 2 |第一个结构是通过Susy古典BRST综合体，第二个是通过Susy Drinfeld-Sokolov Hamiltonian减少的。我们表明，这两种方法引起了同构Susy Poisson顶点代数。作为第一部分的超对称类似物，我们计算发生器之间的显式发电机和泊松支架。
In the first part of this paper, we discuss the classical W-algebra $\mathcal{W}(\mathfrak{g}, F)$ associated with a Lie superalgebra $\mathfrak{g}$ and the nilpotent element $F$ in an $\mathfrak{sl}_2$-triple. We find a generating set of $\mathcal{W}(\mathfrak{g}, F)$ and compute the Poisson brackets between them. In the second part, which is the main part of the paper, we discuss supersymmetric classical W-algebras. We introduce two different constructions of a supersymmetric classical W-algebra $\mathcal{W}(\mathfrak{g}, f)$ associated with a Lie superalgebra $\mathfrak{g}$ and an odd nilpotent element $f$ in a subalgebra isomorphic to $\mathfrak{osp}(1|2)$. The first construction is via the SUSY classical BRST complex and the second is via the SUSY Drinfeld-Sokolov Hamiltonian reduction. We show that these two methods give rise to isomorphic SUSY Poisson vertex algebras. As a supersymmetric analogue of the first part, we compute explicit generators and Poisson brackets between the generators.
