On automorphisms of CR-submanifolds of complex Hilbert space

摘要

It is shown that there exists only one tolally nondegenerate CR manifold of type (n, ∞) (up to the formal equivalence), and the dimension of its Lie algebra g of positively graded formal tangent vector fields is infinite. Examples of manifolds of type (n, ∞) with algebras of any given in advance finite dimension are presented.