Partial classification of modules for Lie-algebra of diffeomorphisms of d-dimensional torus
نویسنده
چکیده
We consider the Lie-algebra of the group of diffeomorphisms of a ddimensional torus which is also known to be the algebra of derivations on a Laurent polynomial ring A in d commuting variables denoted by DerA. 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 has 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.
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تاریخ انتشار 2003