Polarised Lie groups contactomorphic to stratified groups

Abstract

For a stratified group $G$, we construct a class of polarised Lie groups, which we call modifications of $G$, that are locally contactomorphic to it. Vice versa, we show that if a polarised group is locally contactomorphic to a stratified group $G$, whose Lie algebra has finite Tanaka prolongation, then it must be a modification of $G$.

20 pages; changes from previous version: reorganization of the paper and improvements in the exposition of the results