Poisson Homology of r-Matrix Type Orbits I: Example of Computation
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چکیده
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 CPn-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 CPn-type orbits. In Section 2 we calculate the Poisson homology of Drinfeld–Sklyanin Poisson brackets which belong to the r-matrix Poisson family.
منابع مشابه
Poisson homology of R - matrix type orbits I : example of computation Alexei
The Poisson homology was introduced in [1][9]. There are at least two reasons to study them. The first argument is that one can compute Hochschild complex for a deformed algebra of smooth functions using Poisson homology as the second term in appropriate spectral sequence. The next argument was established not so long time ago. There is a connection between canonical (Poisson homology) complex ...
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