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This article is cited in 8 scientific papers (total in 8 papers)
The vertex algebra $m(1)^+$ and certain affine vertex algebras of level $-1$
Dražen Adamović, Ozren Perše Faculty of Science, Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
Abstract:
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.
Received: March 9, 2012; in final form July 1, 2012; Published online July 8, 2012
Citation:
Dražen Adamović, Ozren Perše, “The vertex algebra $m(1)^+$ and certain affine vertex algebras of level $-1$”, SIGMA, 8 (2012), 040, 16 pp.
Linking options:
https://www.mathnet.ru/eng/sigma717 https://www.mathnet.ru/eng/sigma/v8/p40
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