Linearization of isotropy subalgebra of a transitive Lie algebra of vector fields

Michail Zhitomirskii

Let 𝒜 be a finite-dim transitive Lie algebra of vector field germs at $0\in \R^n$ and let be its isotropy subalgebra. When is diffeomorphic to the isotropy representation j1 (i.e. can be linearized)? I will discuss this question from various points of view and will formulate and explain some unexpected theorems.