On Conormal Lie Algebras of Feigin-Odesskii Poisson Structures

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 Ext’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.