Conformal embeddings of affine vertex algebras in minimal W -algebras I: Structural results
Name
Kac_Conformal embeddings.pdf
Description
Submitted version
Size
369.53 KB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Adamovic, Drazen
Kac, Victor
Frajria, Pierluigi Moseneder
Papi, Paolo
Perse, Ozren
Date Issued
April 2018
Journal
Journal of Algebra
Publisher
Elsevier BV
Citation
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.
Version
Original manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.JALGEBRA.2016.12.005
