Structure of classical (finite and affine) W-algebras
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1404.0715.pdf
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392.11 KB
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Author(s)
De Sole, Alberto
Kac, Victor
Valeri, Daniele
Date Issued
July 2016
Journal
Journal of the European Mathematical Society
Publisher
European Mathematical Publishing House
Citation
De Sole, Alberto, et al. “Structure of Classical (Finite and Affine) W-Algebras.” Journal of the European Mathematical Society, vol. 18, no. 9, 2016, pp. 1873–908.
Version
Original manuscript
Abstract
First, we derive an explicit formula for the Poisson bracket of the classical finite W- Algebra W[superscript fin] (g, f), the algebra of polynomial functions on the Slodowy slice associated to a simple Lie algebra g and its nilpotent element f . On the other hand, we produce an explicit set of generators and we derive an explicit formula for the Poisson vertex algebra structure of the classical affine W- Algebra W(g, f). As an immediate consequence, we obtain a Poisson algebra isomorphism between W[superscript fin] (g, f) and the Zhu algebra of W(g, f).We also study the generalized Miura map for classical W- Algebras. Keywords: W-algebra, Poisson algebra, Poisson vertex algebra, Slodowy slice, Hamiltonian reduction, Zhu algebra, Miura map
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.4171/JEMS/632
