The homotopy type of invariant control set

Authors

  • Alexandre J. Santana Universidade Estadual de Maringá.

DOI:

https://doi.org/10.4067/S0716-09172002000300002

Keywords:

Semigroups, Lie groups, homotopy types, control sets, flag manifolds, semigrupos, grupos de Lie, tipos de homotopía, conjuntos de control, variedades bandera.

Abstract

Let G be a noncompact semi-simple Lie group, consider S a semigroup which contains a large Lie semigroup. We computer the homotopy type ??(C), where C is the invariant control set of the homogeneous space G=P with P ? G a parabolic subgroup of G.

Author Biography

Alexandre J. Santana, Universidade Estadual de Maringá.

Departamento de Matemática.

References

[1] C. J. Braga Barros e L. A. B. San Martin, On the action of semigroups in fiber bundles. Mat. Contemp. 13, pp. 1-19, (1997).

[2] J. Hilgert and K.-H. Neeb, Lie semigroups and their applications. Lecture Notes in Math. 1552. Springer-Verlag 1993.

[3] J. E. Humphreys, Reflection groups and coxeter groups. Cambridge studies in advanced mathematics 29 (1990).

[4] C. R. F. Maunder, Algebraic Topology. Van Nostrand (1970).

[5] D. Mittenhuber, On maximal Lie semigroups in real hyperbolic geometry.

[6] L. A. B. San Martin, Invariant control sets on flag manifolds. Mathematics of Control, Signals, and Systems 6, pp. 41-61, (1993).

[7] L. A. B. San Martin, Algebras de Lie. Editora da Unicamp (1999).

[8] L. A. B. San Martin, Maximal semigroups in semi-simple Lie groups. Trans. Amer. Math. Soc. To appear.

[9] L. A. B. San Martin, Nonexistence of invariant semigroups in affine symmetric spaces. Math. Ann. To appear.

[10] L. A. B San Martin and A. J. Santana, The homotopy type of Lie semigroups in semi-simple Lie groups. Monatsh. Math. To appear.

[11] L. A. B. San Martin and P. A. Tonelli, Semigroup actions on homogeneous spaces. Semigroup Forum 50, pp. 59-88, (1995).

[12] G. Warner, Harmonic analysis on semi-simple Lie groups I. SpringerVerlag (1972).

Published

2017-05-22

How to Cite

[1]
A. J. Santana, “The homotopy type of invariant control set”, Proyecciones (Antofagasta, On line), vol. 21, no. 3, pp. 225-243, May 2017.

Issue

Section

Artículos