Algebraic quotients of compact group actions

摘要

Let K be a compact Lie group and X a real algebraic (or real analytic) K-variety. We find conditions under which the quotient X/K is again algebraic (real analytic), and we compare properties of X and X/K, including coherence and smoothness. For example, if L is a closed subgroup of K and A is a real affine algebraic L-manifold, then the twisted product K *(L) A is naturally an affine real algebraic K-manifold. (C) 2001 Academic Press. [References: 19]