Resumen de Non-linear Lie conformal algebras with three generators

Bojko Bakalov, Alberto De Sole

• 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.