Structure of classical (finite and affine) W-algebras

De Sole, A., Kac, V. G. and Valeri, D. (2016) Structure of classical (finite and affine) W-algebras. Journal of the European Mathematical Society, 18(9), pp. 1873-1908. (doi: 10.4171/JEMS/632)

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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 classical W-algebras.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Valeri, Dr Daniele
Authors: De Sole, A., Kac, V. G., and Valeri, D.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of the European Mathematical Society
Publisher:European Mathematical Society
ISSN:1435-9855
ISSN (Online):1435-9863
Published Online:25 July 2016

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