FINITENESS PROPERTIES OF FORMAL LIE GROUP ACTIONS

Abstract

Following the 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.