Giuseppe Dito and Moshe Flato
Generalized Abelian Deformations: Application to Nambu Mechanics
(54K, LaTeX with AMS-Fonts)

ABSTRACT.  We study Abelian generalized deformations of the usual product of polynomials 
introduced in mp_arc/96-39. We construct an explicit example for the case of 
$\frak{su}(2)$ which provides a tentative of a quantum-mechanical description 
of Nambu Mechanics on ${\Bbb R}^3$. By introducing the notions of strong and 
weak triviality of generalized deformations, we show that the Zariski product 
is never trivial in either sense, while the example constructed here in a
quantum-mechanical context is only strongly non-trivial.