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 classicalW- Algebras.

Structure of classical (finite and affine) W-algebras / DE SOLE, Alberto; V., Kac; Valeri, Daniele. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - STAMPA. - 18:(2016), pp. 1873-1908. [10.4171/JEMS/632]

Structure of classical (finite and affine) W-algebras

DE SOLE, ALBERTO;VALERI, DANIELE
2016

Abstract

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 classicalW- Algebras.
2016
Hamiltonian reduction; Miura map; Poisson algebra; Poisson vertex algebra; Slodowy slice; W- Algebra; Zhu algebra
01 Pubblicazione su rivista::01a Articolo in rivista
Structure of classical (finite and affine) W-algebras / DE SOLE, Alberto; V., Kac; Valeri, Daniele. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - STAMPA. - 18:(2016), pp. 1873-1908. [10.4171/JEMS/632]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/782743
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