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Poisson homology of r-matrix type orbits I: example of computation

Alexei Kotov
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Abstract

In this paper we consider the Poisson algebraic structure associated with a classical $r$-matrix, i.e. with a solution of the modified classical Yang--Baxter equation. In Section 1 we recall the concept and basic facts of the $r$-matrix type Poisson orbits. Then we describe the $r$-matrix Poisson pencil (i.e the pair of compatible Poisson structures) of rank 1 or $CP^n$-type orbits of $SL(n,C)$. Here we calculate symplectic leaves and the integrable foliation associated with the pencil. We also describe the algebra of functions on $CP^n$-type orbits. In Section 2 we calculate the Poisson homology of Drinfeld--Sklyanin Poisson brackets which belong to the $r$-matrix Poisson family.

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BibTeXRIS

Alexei Kotov. 1998-12-25. Poisson homology of r-matrix type orbits I: example of computation. https://doi.org/10.2991/jnmp.1999.6.4.2

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