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Non-linear Lie conformal algebras with three generators

Authors:	Bojko Bakalov Alberto De Sole

Institution:	(1) Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA;(2) Dipartimento di Matematica, Universitá di Roma “La Sapienza”, Piaz.le Aldo Moro 5, 00185 Roma, Italy

Abstract:	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 $R^d_{-1} (d \in\mathbb{N})$ and the corresponding freely generated vertex algebras $V^d_{-1}$ , 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 $V^d_{-1}$ extending the Wakimoto realization of $\widehat{s\ell}_{2}$ at the critical level, and we compute their Zhu algebras. Dedicated to our teacher Victor Kac on the occasion of his 65th birthday

Keywords:	Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 17B69 Secondary 81R10
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