Algebraic Quotients of Compact Group Actions
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 rea...
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| Published in | Journal of algebra Vol. 244; no. 2; pp. 365 - 378 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
15.10.2001
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| Online Access | Get full text |
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| Summary: | 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*LA is naturally an affine real algebraic K-manifold. |
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| ISSN: | 0021-8693 1090-266X |
| DOI: | 10.1006/jabr.2001.8778 |