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(-1)(d) (d is an element of 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(-1)(d) extending the Wakimoto realization of (sl(2)) over cap at the critical level, and we compute their Zhu algebras.

Non-linear Lie conformal algebras with three generators / Bojko, Bakalov; DE SOLE, Alberto. - In: SELECTA MATHEMATICA. - ISSN 1022-1824. - STAMPA. - 14:2(2009), pp. 163-198. [10.1007/s00029-008-0058-8]

Non-linear Lie conformal algebras with three generators

DE SOLE, ALBERTO
2009

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(-1)(d) (d is an element of 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(-1)(d) extending the Wakimoto realization of (sl(2)) over cap at the critical level, and we compute their Zhu algebras.
2009
affine kac-moody algebra; affne kac moody algebra; non-linear lie conformal algebra; vertex algebr; vertex algebra
01 Pubblicazione su rivista::01a Articolo in rivista
Non-linear Lie conformal algebras with three generators / Bojko, Bakalov; DE SOLE, Alberto. - In: SELECTA MATHEMATICA. - ISSN 1022-1824. - STAMPA. - 14:2(2009), pp. 163-198. [10.1007/s00029-008-0058-8]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/143732
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