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 |
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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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