DOI QR코드

DOI QR Code

SOME REMARKS ON SEMIALGEBRAIC TRANSFORMATION GROUPS

Park, Dae Heui

  • Received : 2012.07.27
  • Accepted : 2012.09.10
  • Published : 2012.12.25

Abstract

Let G be a semialgebraic group and M a proper semi-algebraic G-set which is locally complete. In this paper we show that the orbit space M/G has a semialgebraic structure such that the orbit map is semialgebraic.

Keywords

transformation groups;semialgebraic sets;orbit spaces

References

  1. J. Bochnak, M. Coste and M.-F. Roy, Real Agebraic Geometry, Erg. der Math. und ihrer Grenzg., vol. 36, Springer-Verlag, Berlin Heidelberg, 1998.
  2. G. E. Bredon, Introduction to Compact Transformation Groups, Pure and Ap- plied Mathematics, vol. 46, Academic Press, New York, 1972.
  3. G. W. Brumfiel, Quotient space for semialgebraic equivalence relation, Math. Z. 195 (1987), 69-78. https://doi.org/10.1007/BF01161599
  4. H. Delfs and M. Knebusch, Locally Semialgebraic Spaces, Lecture Notes in Math. 1173, Springer, Berlin, 1985.
  5. T. tom Dieck, Transformation Groups, Walter de Gruyter, New York, 1987.
  6. R. S. Palais, On the existence of slices for actions of non-compact Lie groups, Ann. of Math. 73(2) (1961), 295-323. https://doi.org/10.2307/1970335
  7. Y. Peterzil, A. Pillay, and S. Starchenko, Definably simple groups in o-minimal structures, Trans. Amer. Math. Soc. 352(10) (2002), 4397-4419.
  8. A. Pillay, On groups and fields definable in o-minimal structures, J. Pure Applied Algebra 53 (1988), 239-255. https://doi.org/10.1016/0022-4049(88)90125-9
  9. R. Robson, Embedding semi-algebraic spaces, Math. Z. 183 (1983), 365-370. https://doi.org/10.1007/BF01176477
  10. C. Scheiderer, Quotients of semi-algebraic spaces, Math. Z. 201 (1989), 249-271. https://doi.org/10.1007/BF01160681

Acknowledgement

Supported by : Chonnam National University