Partial classification of modules for Lie-algebra of diffeomorphisms of d-dimensional torus
Partial classification of modules for Lie-algebra of diffeomorphisms of d-dimensional torus
复制标题
DOI：
10.1063/1.1769104
复制
发表时间：
2003-12
影响因子：
1.3
通讯作者：
S. E. Rao;Field Theory;Di Francesco;Senechal Mathieu
中科院分区：
文献类型：
--
作者：
S. E. Rao;Field Theory;Di Francesco;Senechal Mathieu
We consider the Lie-algebra of the group of diffeomorphisms of a d-dimensional torus which is also known to be the algebra of derivations on a Laurent polynomial ring A in d commuting variables denoted by Der A. The universal central extension of Der A for d=1 is the so-called Virasoro algebra. The connection between Virasoro algebra and physics is well known. See, for example, the book on Conformal Field Theory by Di Francesco, Mathieu, and Senechal. In this paper we classify (A, Der A) modules which are irreducible and have finite dimensional weight spaces. Earlier Larsson constructed a large class of modules, the so-called tensor fields, based on gld modules which are also A modules. We prove that they exhaust all (A, Der A) irreducible modules.
