Vacuum Vector Representations of the Virasoro Algebra
Vacuum Vector Representations of the Virasoro Algebra
复制标题
Virasoro 代数的真空向量表示
DOI：
10.1007/978-1-4613-9550-8_22
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发表时间：
1985
影响因子：
5.4
通讯作者：
A. Rocha
中科院分区：
文献类型：
--
作者：
A. Rocha
最近，许多注意力集中在某些无限维李代数上，因为它们在一些物理理论中的重要性以及它们的数学理论的丰富性。这些代数之一是维拉索罗代数。 Virasoro 代数在双弦模型理论中为物理学家所知（参见[25]）。我们所知的第一本关于 Virasoro 代数的数学参考文献是 Gelfand 和 Fuchs 的著作 [9]。他们证明了圆上多项式向量场的李代数 v 的第二上同调是一维的。使用这个可以表明 Virasoro 代数是 v 的通用中心扩展 \( \mathop{v}\limits^{ \wedge } \) （参见下面的§4）。 Virasoro 代数后来被实现为 Kac-Moody 代数表示空间上的算子代数（参见 [5,3,11,17]），这在某种程度上让人想起它早期在对偶模型中的引入。
A lot of attention has been focused lately on certain infinite dimensional Lie algebras for their importance in some physical theories as well as the richness of their mathematical theories. One of these algebras is the Virasoro algebra. The Virasoro algebra is known to physicists in the theory of dual string models (cf. [25]). The first mathematical reference on the Virasoro algebra that is known to us is by Gelfand and Fuchs [9]. They proved that the second cohomology of the Lie algebra v of polynomial vector fields on the circle is one-dimensional. Using this one can show that the Virasoro algebra is the universal central extension \( \mathop{v}\limits^{ \wedge } \) of v (see §4 below). The Virasoro algebra was later realized as an algebra of operators on the representation space of a Kac-Moody algebra (cf. [5, 3, 11, 17]), in a way reminiscent of its earlier introduction in dual models.