We are interested in Poisson structures to transverse nilpotent adjoint orbits in a complex semi-simple Lie algebra, and we study their polynomial nature. Furthermore, in the case of $sl_n$, we construct some families of nilpotent orbits with quadratic transverse structures.

Keywords:

nilpotent adjoint orbits, conormal orbits, Poisson transverse structure nilpotent adjoint orbits, conormal orbits, Poisson transverse structure

MSC Classifications:

22E, 53D show english descriptions unknown classification 22E
unknown classification 53D 22E - unknown classification 22E
53D - unknown classification 53D

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