Left-symmetric conformal algebras and vertex algebras

• Yanyong Hong ^[2] ; Fang Li ^[1]
  1. [1] Zhejiang University

     Zhejiang University

     China

     
  2. [2] Zhejiang Agriculture and Forestry University, PR China
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 8 (August 2015), 2015, págs. 3543-3567
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.12.012
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• Resumen

  • A vertex algebra is an algebraic counterpart of a two-dimensional conformal field theory. By an equivalent characterization of vertex algebra using Lie conformal algebra and left-symmetric algebra given by Bakalov and Kac in [3], in studying vertex algebra, we have to deal with such a question: Do there exist compatible left-symmetric algebra structures on a class of special Lie algebras named formal distribution Lie algebras? In this paper, we study this question. We introduce the definitions of left-symmetric conformal algebra and Novikov conformal algebra. Many examples of these algebras are obtained. As an application, we present a construction of vertex algebra using left-symmetric conformal algebra.