N-point Virasoro Algebras and Their Modules of Densities

2013/08/30 by Ben Cox, Xiangqian Guo, Cox, Ben +6
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.RT

paper · pdf · doi:10.48550/arxiv.1308.6815

arxiv created 2013/08/30 · arxiv updated 2013/09/02

Abstract

In this paper we introduce and study n-point Virasoro algebras, \W_a, which are natural generalizations of the classical Virasoro algebra and have as quotients multipoint genus zero Krichever-Novikov type algebras. We determine necessary and sufficient conditions for the latter two such Lie algebras to be isomorphic. Moreover we determine their automorphisms, their derivation algebras, their universal central extensions, and some other properties. The list of automorphism groups that occur is C_n, D_n, A₄, S₄ and A₅. We also construct a large class of modules which we call modules of densities, and determine necessary and sufficient conditions for them to be irreducible.

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