Non-linear Lie conformal algebras with three generators
Mathematical Physics
2015-12-18 v2 math.MP
Quantum Algebra
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 and the corresponding freely generated vertex algebras V_{-1}^d, 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 the affine vertex algebra of sl_2 at the critical level, and we compute their Zhu algebras.
Cite
@article{arxiv.0710.2281,
title = {Non-linear Lie conformal algebras with three generators},
author = {Bojko Bakalov and Alberto De Sole},
journal= {arXiv preprint arXiv:0710.2281},
year = {2015}
}
Comments
36 pages, v2 minor changes