On symmetric semialgebraic sets and orbit spaces

• Autorzy: Ludwig Bröcker
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1998
• Tom: 44
• Numer: 1
• Strony: 37-50

Daty

wydano

1998

Twórcy

autor

Ludwig Bröcker

• Mathematisches Institut, Universität Münster, Einsteinstraß e 62, D-48149 Münster, Germany

Bibliografia

• [A-B-R] C. Andradas, L. Bröcker, J. Ruiz, Constructible Sets in Real Geometry, Ergeb. Math. Grenzgeb. (3) 33, Springer, Berlin, 1996.
• [Be1] E. Becker, Hereditarily-Pythagorean Fields and Orderings of Higher Level, Monografias de Matemática 29, Instituto de Matématica Pura et Aplicada, Rio de Janeiro, 1978.
• [Be2] E. Becker, On the real spectrum of a ring and its applications to semi-algebraic geometry, Bull. Amer. Math. Soc. (N.S.) 15 (1986), 19-60.
• [B-C-R] J. Bochnak, M. Coste, M.-F. Roy, Géométrie algébrique réelle, Ergeb. Math. Grenzgeb. (3) 12, Springer, Berlin, 1987.
• [B] L. Bröcker, On basic semialgebraic sets, Exposition. Math. 9 (1991), 289-334.
• [DM-I] F. De Meyer, E. Ingraham, Separable Algebras over Commutative Rings, Lecture Notes in Math. 181, Springer, Berlin, 1971.
• [Di-Dr] J. Diller, A. Dress, Zur Galoistheorie pythagoreischer Körper, Arch. Math. (Basel) 16 (1965), 148-152.
• [Kn-Schei] M. Knebusch, C. Scheiderer, Einführung in die reelle Algebra, Vieweg, Braunschweig, 1989.
• [Kr] H. Kraft, Geometrische Methoden in der Invariantentheorie, Aspects of Math. D1, Vieweg, Braunschweig, 1985.
• [Lu] D. Luna, Slices étales, in: Sur les groupes algébriques, Bull. Soc. Math. France, Mémoire 33, Paris, 1973, 81-105.
• [Mar] M. Marshall, Minimal generation of basic sets in the real spectrum of a commutative ring, in: Recent Advances in Real Algebraic Geometry and Quadratic Forms, Contemp. Math. 155, Amer. Math. Soc., Providence, 1994, 207-219.
• [Pr] A. Prestel, Lectures on Formally Real Fields, Lecture Notes in Math. 1093, Springer, Berlin, 1984.
• [Pro-Schw] C. Procesi, G. Schwarz, Inequalities defining orbit spaces, Invent. Math. 81 (1985), 539-554.
• [Schei1] C. Scheiderer, Stability index of real varieties, Invent. Math. 97 (1989), 467-483.
• [Schei2] C. Scheiderer, Spaces of orderings of fields under finite extensions, Manuscripta Math. 72 (1991), 27-47.
• [Schw] G. Schwarz, The topology of algebraic quotients, in: Topological Methods in Algebraic Transformation Groups, Progr. Math. 80, Birkhäuser, Boston, 1989, 135-152.
• [Slo-Kno] P. Slodowy, Der Scheibensatz für algebraische Transformationsgruppen, mit einem Anhang von F. Knop, in: Algebraische Transformationsgruppen und Invariantentheorie, DMV Sem. 13, Birkhäuser, Basel, 1989, 89-114.
• [Weyl] H. Weyl, The Classical Groups, 2nd ed., Princeton University Press, 1946.