Poisson Homology of r-Matrix Type Orbits I: Example of Computation

DOI

10.2991/jnmp.1999.6.4.2How to use a DOI?

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 Yang­Baxter 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 Drinfeld­Sklyanin Poisson brackets which belong to the r-matrix Poisson family.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Alexei Kotov
PY  - 1999
DA  - 1999/11/01
TI  - Poisson Homology of r-Matrix Type Orbits I: Example of Computation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 365
EP  - 383
VL  - 6
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1999.6.4.2
DO  - 10.2991/jnmp.1999.6.4.2
ID  - Kotov1999
ER  -