Israel Journal of Mathematics

, Volume 129, Issue 1, pp 29–60

Polynomial mappings of groups

Article

DOI: 10.1007/BF02773152

Cite this article as:
Leibman, A. Isr. J. Math. (2002) 129: 29. doi:10.1007/BF02773152

Abstract

A mapping ϕ of a groupG to a groupF is said to be polynomial if it trivializes after several consecutive applications of operatorsDh,hG, defined byDhϕ(g)=ϕ(g)−1ϕ(gh). We study polynomial mappings of groups, mainly to nilpotent groups. In particular, we prove that polynomial mappings to a nilpotent group form a group with respect to the elementwise multiplication, and that any polynomial mappingGF to a nilpotent groupF splits into a homomorphismGG’ to a nilpotent groupG’ and a polynomial mappingG’F. We apply the obtained results to prove the existence of the compact/weak mixing decomposition of a Hilbert space under a unitary polynomial action of a finitely generated nilpotent group.

Copyright information

© Hebrew University 2002

Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA