%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