Finiteness properties of formal Lie group actions

2014/05/21 by Binyamini, Gal
#32H50 #37C85 #57S20 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1405.5567

Abstract

Following ideas of Arnold and Seigal-Yakovenko, we prove that the space of matrix coefficients of a formal Lie group action belongs to a Noetherian ring. Using this result we extend the uniform intersection multiplicity estimates of these authors from the abelian case to general Lie groups. We also demonstrate a simple new proof for a jet-determination result of Baouendi et. al. In the second part of the paper we use similar ideas to prove a result on embedding formal diffeomorphisms in one-parameter groups extending a result of Takens. In particular this implies that the results of Arnold and Seigal-Yakovenko are formal consequence of our result for Lie groups.

Related

• Applications of Lie ring methods to group theory
• Algorithms for group actions in arbitrary characteristic and a problem\n in singularity theory
• Pairs of Lie-type and large orbits of group actions on filtered modules.\n (A characteristic-free approach to finite determinacy.)
• Aut(Fn) actions on representation spaces
• The finiteness theorem for invariants of a finite group (translation of Emmy Noether's "Der Endlichkeitsatz der Invarianten endlicher Gruppen")