Non-linear Lie conformal algebras with three generators

• Bojko Bakalov ^[1] ; Alberto De Sole ^[2]
  1. [1] North Carolina State University

     North Carolina State University

     Township of Raleigh, Estados Unidos

     
  2. [2] Università de Roma La Sapienza

     Università de Roma La Sapienza

     Roma Capitale, Italia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 14, Nº. 2, 2009, págs. 163-198
• Idioma: inglés
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• Resumen

  • We classify certain non-linear Lie conformal algebras with three generators, which can be viewed as deformations of the current Lie conformal algebra of sℓ 2. In doing so we discover an interesting 1-parameter family of non-linear Lie conformal algebras Rd−1(d∈N) and the corresponding freely generated vertex algebras Vd−1 , which includes for d = 1 the affine vertex algebra of sℓ 2 at the critical level k = –2. We construct free-field realizations of the algebras Vd−1 extending the Wakimoto realization of sℓˆ2 at the critical level, and we compute their Zhu algebras.