Geodesic
Semigroups in Semi-Simple Lie Groups: Flag Type and Estimation of Cocycles
Adriano Da Silva1 ; Luiz A. B. San Martin2 ; Joao V. Uzita3, 4
1Departamento de Matemática, Universidad de Tarapacá, Iquique, Chile
2Instituto de Matemática, Universidade Estadual de Campinas, Sao Paulo, Brasil
3(1) Departamento de Matemática, Universidad de Tarapacá, Arica, Chile
4(2) Instituto de Matemática, Universidade Estadual de Campinas, Sao Paulo, Brasil
Journal of Lie Theory, Tome 35 (2025) no. 3, pp. 557-571

Voir la notice de l'article provenant de la source Heldermann Verlag

The flag type of a semigroup S of a noncompact semisimple Lie group is an algebraic tool related to the geometry of the invariant control set determined by S on the flag manifolds of G. In the present paper, we show that it is possible to recover the flag type by studying the existence of lower bounds for cocycles on the maximal flag manifold.
Classification : 20M20, 22E46, 14M15
Mots-clés : Semigroups, semisimple Lie groups, flag manifolds, cocycles

Adriano Da Silva  1   ; Luiz A. B. San Martin  2   ; Joao V. Uzita  3 , 4

1 Departamento de Matemática, Universidad de Tarapacá, Iquique, Chile
2 Instituto de Matemática, Universidade Estadual de Campinas, Sao Paulo, Brasil
3 (1) Departamento de Matemática, Universidad de Tarapacá, Arica, Chile
4 (2) Instituto de Matemática, Universidade Estadual de Campinas, Sao Paulo, Brasil 
Adriano Da Silva; Luiz A. B. San Martin; Joao V. Uzita. Semigroups in Semi-Simple Lie Groups: Flag Type and Estimation of Cocycles. Journal of Lie Theory, Tome 35 (2025) no. 3, pp. 557-571. http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a4/
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     author = {Adriano Da Silva and Luiz A. B. San Martin and Joao V. Uzita},
     title = {Semigroups in {Semi-Simple} {Lie} {Groups:} {Flag} {Type} and {Estimation} of {Cocycles}},
     journal = {Journal of Lie Theory},
     pages = {557--571},
     year = {2025},
     volume = {35},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a4/}
}
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