%0 Journal Article
%T The Vertex Algebra M(1)+ and Certain Affine Vertex Algebras of Level  1
%A Dra£¿en Adamovi£¿
%A Ozren Per£¿e
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2012
%I National Academy of Science of Ukraine
%X We give a coset realization of the vertex operatoralgebra $M(1)^+$ with central charge $ell$. We realize $M(1) ^+$as a commutant of certain affine vertex algebras of level $-1$ inthe vertex algebra $L_{C_{ell} ^{(1)}}(- frac{1}{2}Lambda_0)otimes L_{C_{ell} ^{(1)}}(- frac{1}{2}Lambda_0)$. We show thatthe simple vertex algebra $L_{C_{ell} ^{(1)}}(-Lambda_0)$ can be(conformally) embedded into $L_{A_{2 ell -1} ^{(1)}} (-Lambda_0)$and find the corresponding decomposition. We also study certaincoset subalgebras inside $L_{C_{ell} ^{(1)}}(-Lambda_0)$.
%K vertex operator algebra
%K affine Kac-Moody algebra
%K coset vertex algebra
%K conformal embedding
%K W-algebra
%U http://dx.doi.org/10.3842/SIGMA.2012.040