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

作者：dos Santos Ariane Luzia; San Martin Luiz A B^*

来源：Semigroup Forum, 2017, 95(2): 259-280.

DOI：10.1007/s00233-016-9798-5

• Semigroup generators of groups
• Semi-simple Lie groups
• Flag manifolds

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.

• 出版日期2017-10