Structure of classical (finite and affine) -algebras
Alberto De Sole
Università di Roma La Sapienza, ItalyVictor G. Kac
Massachusetts Institute of Technology, Cambridge, USADaniele Valeri
SISSA, Trieste, Italy
![Structure of classical (finite and affine) $\mathcal W$-algebras cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jems-volume-18-issue-9.png&w=3840&q=90)
Abstract
First, we derive an explicit formula for the Poisson bracket of the classical finite -algebra , the algebra of polynomial functions on the Slodowy slice associated to a simple Lie algebra and its nilpotent element . 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 -algebra . As an immediate consequence, we obtain a Poisson algebra isomorphism between and the Zhu algebra of . We also study the generalized Miura map for classical -algebras.
Cite this article
Alberto De Sole, Victor G. Kac, Daniele Valeri, Structure of classical (finite and affine) -algebras. J. Eur. Math. Soc. 18 (2016), no. 9, pp. 1873–1908
DOI 10.4171/JEMS/632