The homotopy type of invariant control set
DOI:
https://doi.org/10.4067/S0716-09172002000300002Keywords:
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.References
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[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.
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