Abstract:
We examine a family of twists of the complex polynomial ring on n generators by a non-semisimple automorphism. In particular, we consider the case where the automorphism is represented by a single Jordan block. The multiplication in the twist determines a Poisson structure on affine n-space. We demonstrate that the primitive ideals in the twist are parameterized by the symplectic leaves associated to this Poisson structure. Moreover, the symplectic leaves are determined by the orbits of a regular unipotent subgroup of the complex general linear group.