Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-16T11:36:55.085Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite Groups Generated by Involutions on Lagrangian Planes of C2

Published online by Cambridge University Press:  20 November 2018

E. Falbel
E. Falbel*
Affiliation:
Institut de Mathématiques Université Pierre et Marie Curie 4, place Jussieu 75252 Paris France, email: falbel@math.jussieu.fr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We classify finite subgroups of $\text{SO}\left( 4 \right)$ generated by anti-unitary involutions. They correspond to involutions fixing pointwise a Lagrangian plane. Explicit descriptions of the finite groups and the configurations of Lagrangian planes are obtained.

Keywords

22E4053D99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 4 , 01 December 2001 , pp. 408 - 419
Copyright
Copyright © Canadian Mathematical Society 2001

References

[C1] Coxeter, H. S. M., Groups generated by unitary reflections of period two. Canad. J. Math. 9 (1957), 243–272.Google Scholar
[C2] Coxeter, H. S. M., Regular Complex Polytopes. Cambridge University Press, 1991.Google Scholar
[Cr] Crowe, D. W., The groups of regular complex polygons. Canad. J. Math. 13 (1961), 149–156.Google Scholar
[D] Du Val, P., Homographies, Quaternions and Rotations. Oxford Mathematical Monographs, Oxford, 1964.Google Scholar
[FZ] Falbel, E. and Zocca, V., A Poincaré's polyhedron theorem for complex hyperbolic geometry. J. Reine Angew.Math. 516 (1999), 133–158.Google Scholar
[FK] Falbel, E. and Koseleff, P.-V., Flexibility of the ideal triangle group in complex hyperbolic geometry. Topology, to appear.Google Scholar
[G] Goldman, W., Complex Hyperbolic Geometry. Oxford Mathematical Monographs, Oxford Science Publications, 1999.Google Scholar
[ST] Shephard, G. C. and Todd, J. A., Finite unitary reflection groups. Canad. J. Math. 6 (1954), 274–304.Google Scholar