Symplectic Leaves of W-Algebras From the Reduced Kac–Moody Point of View

Bajnok, Z.; Nógrádi, D.

doi:10.7546/giq-2-2001-99-109

VOL. 2 | 2001 Symplectic Leaves of W-Algebras From the Reduced Kac–Moody Point of View

Chapter Author(s) Z. Bajnok, D. Nógrádi

Editor(s) Ivaïlo M. Mladenov, Gregory L. Naber

Geom. Integrability & Quantization, 2001: 99-109 (2001) DOI: 10.7546/giq-2-2001-99-109

Abstract

The symplectic leaves of W-algebras are the intersections of the symplectic leaves of the Kac-Moody algebras and the hypersurface of the second class constraints, which define the $W-$algebra. This viewpoint enables us to classify the symplectic leaves and also to give a representative for each of them. The case of the $W_2$ (Virasoro) algebra is investigated in detail, where the positivity of the energy functional is also analyzed.