Geodesic
Structure of classical (finite and affine) $\mathcal W$-algebras
Journal of the European Mathematical Society, Tome 18 (2016) no. 9, pp. 1873-1908.

Voir la notice de l'article provenant de la source EMS Press

First, we derive an explicit formula for the Poisson bracket of the classical finite W-algebra Wfin(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 Wfin(g,f) and the Zhu algebra of W(g,f). We also study the generalized Miura map for classical W-algebras.
DOI : 10.4171/jems/632
Classification : 17-XX, 37-XX
Keywords: W-algebra, Poisson algebra, Poisson vertex algebra, Slodowy slice, Hamiltonian reduction, Zhu algebra, Miura map 
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     author = {Alberto De Sole and Victor G. Kac and Daniele Valeri},
     title = {Structure of classical (finite and affine) $\mathcal W$-algebras},
     journal = {Journal of the European Mathematical Society},
     pages = {1873--1908},
     publisher = {mathdoc},
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Alberto De Sole; Victor G. Kac; Daniele Valeri. Structure of classical (finite and affine) $\mathcal W$-algebras. Journal of the European Mathematical Society, Tome 18 (2016) no. 9, pp. 1873-1908. doi : 10.4171/jems/632. http://geodesic.mathdoc.fr/articles/10.4171/jems/632/

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