Conformal embeddings of affine vertex algebras in minimal W -algebras I: Structural results
We find all values of k∈C, for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra Wk(g,θ) is conformal, where g is a basic simple Lie superalgebra and −θ its minimal root. In particular, it turns out that if Wk(g,θ) does not collapse to its affine part, then the p...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier BV
2019
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| Online Access: | https://hdl.handle.net/1721.1/122979 |
| _version_ | 1826215540349206528 |
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| author | Adamovic, Drazen Kac, Victor Frajria, Pierluigi Moseneder Papi, Paolo Perse, Ozren |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Adamovic, Drazen Kac, Victor Frajria, Pierluigi Moseneder Papi, Paolo Perse, Ozren |
| author_sort | Adamovic, Drazen |
| collection | MIT |
| description | We find all values of k∈C, for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra Wk(g,θ) is conformal, where g is a basic simple Lie superalgebra and −θ its minimal root. In particular, it turns out that if Wk(g,θ) does not collapse to its affine part, then the possible values of these k are either −[Formula presented], where h∨ is the dual Coxeter number of g for the normalization (θ,θ)=2. As an application of our results, we present a realization of simple affine vertex algebra V−[Formula presented](sl(n+1)) inside the tensor product of the vertex algebra W[Formula presented](sl(2|n),θ) (also called the Bershadsky–Knizhnik algebra) with a lattice vertex algebra. |
| first_indexed | 2024-09-23T16:34:15Z |
| format | Article |
| id | mit-1721.1/122979 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:34:15Z |
| publishDate | 2019 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1229792022-09-29T20:09:48Z Conformal embeddings of affine vertex algebras in minimal W -algebras I: Structural results Adamovic, Drazen Kac, Victor Frajria, Pierluigi Moseneder Papi, Paolo Perse, Ozren Massachusetts Institute of Technology. Department of Mathematics We find all values of k∈C, for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra Wk(g,θ) is conformal, where g is a basic simple Lie superalgebra and −θ its minimal root. In particular, it turns out that if Wk(g,θ) does not collapse to its affine part, then the possible values of these k are either −[Formula presented], where h∨ is the dual Coxeter number of g for the normalization (θ,θ)=2. As an application of our results, we present a realization of simple affine vertex algebra V−[Formula presented](sl(n+1)) inside the tensor product of the vertex algebra W[Formula presented](sl(2|n),θ) (also called the Bershadsky–Knizhnik algebra) with a lattice vertex algebra. National Science Foundation (U.S.) 2019-11-20T15:44:35Z 2019-11-20T15:44:35Z 2018-04 2019-09-25T14:52:46Z Article http://purl.org/eprint/type/JournalArticle 0021-8693 https://hdl.handle.net/1721.1/122979 Adamović, Dražen et al. "Conformal embeddings of affine vertex algebras in minimal W-algebras I: Structural results." Journal of Algebra 500, 15 (April 2018): 117-152 © 2016 Elsevier Inc. en http://dx.doi.org/10.1016/J.JALGEBRA.2016.12.005 Journal of Algebra Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Adamovic, Drazen Kac, Victor Frajria, Pierluigi Moseneder Papi, Paolo Perse, Ozren Conformal embeddings of affine vertex algebras in minimal W -algebras I: Structural results |
| title | Conformal embeddings of affine vertex algebras in minimal W -algebras I: Structural results |
| title_full | Conformal embeddings of affine vertex algebras in minimal W -algebras I: Structural results |
| title_fullStr | Conformal embeddings of affine vertex algebras in minimal W -algebras I: Structural results |
| title_full_unstemmed | Conformal embeddings of affine vertex algebras in minimal W -algebras I: Structural results |
| title_short | Conformal embeddings of affine vertex algebras in minimal W -algebras I: Structural results |
| title_sort | conformal embeddings of affine vertex algebras in minimal w algebras i structural results |
| url | https://hdl.handle.net/1721.1/122979 |
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