Polynomial mappings of groups |
| |
Authors: | A Leibman |
| |
Institution: | (1) Department of Mathematics, The Ohio State University, 43210-1174 Columbus, OH, USA |
| |
Abstract: | A mapping ϕ of a groupG to a groupF is said to be polynomial if it trivializes after several consecutive applications of operatorsD
h
,h ∈G, defined byD
h
ϕ(g)=ϕ(g)
−1
ϕ(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 mappingG→F to a nilpotent groupF splits into a homomorphismG→G’ 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.
This work was supported by NSF, Grants DMS-9706057 and 0070566. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|