The m-Derivations of Analytic Vector Fields Lie Algebras

Randriambololondrantomalala P

doi:10.4172/1736-4337.1000s2-002

Abstract

We consider a (real or complex) analytic manifold M. Assuming that F is a ring of all analytic functions, full or truncated with respect to the local coordinates on M; we study the (m ≥ 2)-derivations of all involutive analytic distributions over F and their respective normalizers.

Highlights

Introduction and PreliminaryWe know several embedding theorems in differential geometry, some of them are of John F
Certain property on a smooth manifold cannot be true on M, for example the global representation of a smooth function germ theorem
We state that the considered Lie algebras have enough sections more than constant ones in the Lie algebra of all analytic vector fields

Summary

Introduction and Preliminary

We know several embedding theorems in differential geometry, some of them are of John F. Certain property on a smooth manifold cannot be true on M, for example the global representation of a smooth function germ theorem Grabowski had this problem when he studied derivations of the real or complex analytic vector fields Lie algebra cf [5] and he used Stein manifolds to avoid technical difficulties in them. In the end, we discuss the Lie algebras of holomorphic vector fields, especially when the holomorphic manifold is not a Stein one, and Lie algebras of locally polynomial vector fields on an analytic manifold M Their m-derivations as well as their normalizers can be characterized by using some results of Randriambololondrantomalala [7]. J Generalized Lie Theory Appl S2: 002. doi:10.4172/1736-4337.S2-002

John Nash

We set the real analytic vector field

It is permit to use Theorem