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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.21 n.3 Antofagasta dic. 2002

http://dx.doi.org/10.4067/S0716-09172002000300002 

Proyecciones
Vol. 21, N o 3, pp. 199-224, December 2002.
Universidad Católica del Norte
Antofagasta - Chile

THE HOMOTOPY TYPE OF INVARIANT
CONTROL SET

ALEXANDRE J. SANTANA *
Universidade Estadual de Maringá, Brasil

Abstract

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

AMS 2000 subject classification: 20M20, 22E46, 57T99.

Key words: Semigroups, Lie groups, homotopy type, control sets, flag manifolds.

  References

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

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

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

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

[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.        [ Links ]

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

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

Received : June 2002.

Alexandre J. Santana
Universidade Estadual de Maringá
Departamento de Matemática
Caixa Postal 331 87020-900 Maringá Pr.
Brasil.
e-mail: ajsantana@uem.br


*Partially supported by PROCAD/CAPES register n± 0186=00-7

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