On conormal Lie algebras of Feigin–Odesskii Poisson structures

Abstract

The main result of the paper is a description of conormal Lie algebras of Feigin–Odesskii Poisson structures. In order to obtain it, we introduce a new variant of a definition of a Feigin–Odesskii Poisson structure: we define it using a differential on the second page of a certain spectral sequence. In the general case, this spectral sequence computes morphisms and higher ${\mathrm{Ext}}^{\prime }s$ between filtered objects in an Abelian category. Moreover, we use our definition to give another proof of the description of symplectic leaves of Feigin–Odesskii Poisson structures.