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The vertex algebra $m(1)^+$ and certain affine vertex algebras of level $-1$
Symmetry, integrability and geometry: methods and applications, Tome 8 (2012) Cet article a éte moissonné depuis la source Math-Net.Ru

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We give a coset realization of the vertex operator algebra $M(1)^+$ with central charge $\ell$. We realize $M(1)^+$ as a commutant of certain affine vertex algebras of level $-1$ in the vertex algebra $L_{C_{\ell}^{(1)}}(-\frac12\Lambda_0)\otimes L_{C_{\ell} ^{(1)}}(-\frac{1}{2}\Lambda_0)$. We show that the 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 certain coset subalgebras inside $L_{C_{\ell} ^{(1)}}(-\Lambda_0)$.
Keywords: vertex operator algebra, affine Kac–Moody algebra, coset vertex algebra, conformal embedding, $\mathcal W$-algebra. 
@article{SIGMA_2012_8_a39,
     author = {Dra\v{z}en Adamovi\'c and Ozren Per\v{s}e},
     title = {The vertex algebra $m(1)^+$ and certain affine vertex algebras of level $-1$},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2012},
     volume = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a39/}
}
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Dražen Adamović; Ozren Perše. The vertex algebra $m(1)^+$ and certain affine vertex algebras of level $-1$. Symmetry, integrability and geometry: methods and applications, Tome 8 (2012). http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a39/

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