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Communications in Mathematical Physics

, Volume 336, Issue 2, pp 1053–1084 | Cite as

Classical \({\mathcal{W}}\)-Algebras in Types A, B, C, D and G

  • A. I. MolevEmail author
  • E. Ragoucy
Article

Abstract

We produce explicit generators of the classical \({\mathcal{W}}\)-algebras associated with the principal nilpotents in the simple Lie algebras of all classical types and in the exceptional Lie algebra of type G 2. The generators are given by determinant formulas in the context of the Poisson vertex algebras. We also show that the images of the \({\mathcal{W}}\)-algebra generators under the Chevalley-type isomorphism coincide with the elements defined via the corresponding Miura transformations.

Keywords

Cartan Subalgebra Differential Algebra Injective Homomorphism Screening Operator Involutive Automorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia
  2. 2.Laboratoire de Physique Théorique LAPThCNRS and Université de SavoieAnnecy-le-Vieux CedexFrance

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