Journal of Lie Theory 35 (2025), No. 3, 557--571
Copyright Heldermann Verlag 2025
Semigroups in Semi-Simple Lie Groups: Flag Type and Estimation of Cocycles
Adriano Da Silva
Departamento de Matemática, Universidad de Tarapacá, Iquique, Chile
adasilva@academicos.uta.cl
Luiz A. B. San Martin
Instituto de Matemática, Universidade Estadual de Campinas, Sao Paulo, Brasil
smartin@unicamp.br
Joao V. Uzita
(1) Departamento de Matemática, Universidad de Tarapacá, Arica, Chile
(2) Instituto de Matemática, Universidade Estadual de Campinas, Sao Paulo, Brasil
uzita05@gmail.com
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.
Keywords: Semigroups, semisimple Lie groups, flag manifolds, cocycles.
MSC: 20M20, 22E46, 14M15.
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