For a symmetric (= invariant under the action of a compact Lie group G) semialgebraic basic set C, described by s polynomial inequalities, we show, that C can also be written by s + 1 G-invariant polynomials. We also describe orbit spaces for the action of G by a number of inequalities only depending on the structure of G.
@article{bwmeta1.element.bwnjournal-article-bcpv44i1p37bwm,
author = {Br\"ocker, Ludwig},
title = {On symmetric semialgebraic sets and orbit spaces},
journal = {Banach Center Publications},
volume = {43},
year = {1998},
pages = {37-50},
zbl = {0917.14030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv44i1p37bwm}
}
Bröcker, Ludwig. On symmetric semialgebraic sets and orbit spaces. Banach Center Publications, Tome 43 (1998) pp. 37-50. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv44i1p37bwm/
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