Lie Theory

Abstract

In this chapter we define local and global Lie group actions on complex spaces. It is shown that a local action of a Lie group G on a complex space X is real analytic. Such an action gives rise to the Lie homomorphism, which is a map from the Lie algebra of G into the Lie algebra of vector fields on X. The second fundamental theorem of S.Lie states that the local action can be recovered from this homomorphism. We prove this theorem and give some sufficient conditions for a local action to extend to a global one.