Adamović, Dražen; Perše, Ozren The vertex algebra \(M(1)^{+}\) and certain affine vertex algebras of level \(-1\). (English) Zbl 1281.17029 SIGMA, Symmetry Integrability Geom. Methods Appl. 8, Paper 040, 16 p. (2012). Summary: 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 \(L_{C_{\ell} ^{(1)}}(-\tfrac{1}{2}\Lambda_0) \otimes L_{C_{\ell} ^{(1)}}(-\tfrac{1}{2}\Lambda_0)\). 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 \(L_{C_{\ell} ^{(1)}}(-\Lambda_0)\). Cited in 7 Documents MSC: 17B69 Vertex operators; vertex operator algebras and related structures 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 17B68 Virasoro and related algebras Keywords:vertex operator algebra; affine Kac-Moody algebra; coset vertex algebra; conformal embedding; \(\mathcal{W}\)-algebra × Cite Format Result Cite Review PDF Full Text: DOI arXiv