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 SIGMA, 2012, Volume 8, 040, 16 pages (Mi sigma717)

The vertex algebra $m(1)^+$ and certain affine vertex algebras of level $-1$

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.

DOI: https://doi.org/10.3842/SIGMA.2012.040

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Bibliographic databases:

ArXiv: 1006.1752
MSC: 17B69; 17B67; 17B68; 81R10
Received: March 9, 2012; in final form July 1, 2012; Published online July 8, 2012
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Citation: Dražen Adamović, Ozren Perše, “The vertex algebra $m(1)^+$ and certain affine vertex algebras of level $-1$”, SIGMA, 8 (2012), 040, 16 pp.

Citation in format AMSBIB
\Bibitem{AdaPer12} \by Dra{\v z}en Adamovi{\'c}, Ozren Per{\v s}e \paper The vertex algebra $m(1)^+$ and certain affine vertex algebras of level $-1$ \jour SIGMA \yr 2012 \vol 8 \papernumber 040 \totalpages 16 \mathnet{http://mi.mathnet.ru/sigma717} \crossref{https://doi.org/10.3842/SIGMA.2012.040} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2946860} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000306115600001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864858502} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Adamovic D., Perse O., “Some General Results on Conformal Embeddings of Affine Vertex Operator Algebras”, Algebr. Represent. Theory, 16:1 (2013), 51–64
2. Creutzig T., Linshaw A.R., “A Commutant Realization of Odake's Algebra”, Transform. Groups, 18:3 (2013), 615–637
3. Adamovic D., Perse O., “Fusion Rules and Complete Reducibility of Certain Modules for Affine Lie Algebras”, J. Algebra. Appl., 13:1 (2014)
4. D. Adamovic, O. Perse, “On extensions of affine vertex algebras at half-integer levels”, Springer INdAM Series, 19 (2017), 281-298
5. Arakawa T., Jiang C., “Coset Vertex Operator Algebras and W-Algebras of a-Type”, Sci. China-Math., 61:2, SI (2018), 191–206
6. Adamovic D., Kac V.G., Frajria P.M., Papi P., Perse O., “On the Classification of Non-Equal Rank Affine Conformal Embeddings and Applications”, Sel. Math.-New Ser., 24:3 (2018), 2455–2498
7. Creutzig T., Linshaw A.R., “Cosets of Affine Vertex Algebras Inside Larger Structures”, J. Algebra, 517 (2019), 396–438
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