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Formal normal forms of degenerate Poisson structures in dimension 3 are described. The main tool of the study is a spectral sequence previously introduced by the author. In particular, this method allows one to obtain a new proof of the linearizability of Poisson structures with semisimple linear part. However, there are nonlinearizable Poisson structures in dimension 3 as well. [ABSTRACT FROM AUTHOR]

In the paper, formal normal forms of Poisson structures are found. As a consequence, obstructions to the formal linearization of Poisson structures are obtained, which gives a generalization of the Weinstein linearization theorem. Lie-Sklyanin algebras corresponding to Poisson structures with trivial linearization are introduced and studied as well. [ABSTRACT FROM AUTHOR]

For differential operators forming an algebra of a certain class that includes algebras of higher derivatives, a Poisson structure is introduced and the first term of the Hochschild spectral sequence is calculated. [ABSTRACT FROM AUTHOR]