✦ LIBER ✦

Algebraic Quotients of Compact Group Actions

✍ Scribed by Gerald W Schwarz

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 129 KB
Volume: 244
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8778

No coin nor oath required. For personal study only.

✦ Synopsis

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.

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