A method to find generators of a semi-simple Lie group via the topology of its flag manifolds

Author(s)

dos Santos, Ariane Luzia ^[1] ; San Martin, Luiz A. B. ^[2]

Affiliation

^[1] UNESP, FCL, Dept Ciencias Educ, Rodovia Araraquara Jau, Km 1, BR-14800901 Araraquara, SP - Brazil

^[2] Univ Estadual Campinas, Imecc, Dept Matemat, Cidade Univ Zeferino Vaz, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: Semigroup Forum; v. 95, n. 2, p. 259-280, OCT 2017.
• Web of Science Citations: 1

Abstract

In this paper we continue to develop the topological method to get semigroup generators of semi-simple Lie groups. Consider a subset Gamma subset of G that contains a semi-simple subgroup of G(1) of G. If one can show that Gamma does not leave invariant a contractible subset on any flag manifold of G, then Gamma generates G if Ad (Gamma)generates a Zariski dense subgroup of the algebraic group Ad(Gamma) . The proof is reduced to check that some specific closed orbits of in the flag manifolds of G are not trivial in the sense of algebraic topology. Here, we consider three different cases of semi-simple Lie groups G and subgroups G(1) subset of G. (AU)

• FAPESP's process: 07/06896-5 - Geometry of control, dynamical and stochastic systems
• Grantee: Luiz Antonio Barrera San Martin
• Support Opportunities: Research Projects - Thematic Grants