A method to find generators of a semi-simple Lie group via the topology of its flag manifolds
| Autor: | Ariane Luzia dos Santos, Luiz A. B. San Martin |
|---|---|
| Přispěvatelé: | Universidade Estadual Paulista (Unesp), Universidade Estadual de Campinas (UNICAMP) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Algebra and Number Theory
Semigroup Simple Lie group 010102 general mathematics Lie group Topology 01 natural sciences Contractible space 010101 applied mathematics Algebraic group Generalized flag variety Flag manifolds Semi-simple Lie groups 0101 mathematics Invariant (mathematics) Semigroup generators of groups Mathematics |
| Zdroj: | Scopus Repositório Institucional da UNESP Universidade Estadual Paulista (UNESP) instacron:UNESP |
| Popis: | In this paper we continue to develop the topological method to get semigroup generators of semi-simple Lie groups. Consider a subset $$\Gamma \subset G$$ that contains a semi-simple subgroup $$G_{1}$$ 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 $$\mathrm {Ad}\left( \Gamma \right) $$ generates a Zariski dense subgroup of the algebraic group $$\mathrm {Ad}\left( G\right) $$ . The proof is reduced to check that some specific closed orbits of $$G_{1}$$ 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 $$G_{1}\subset G$$ . |
| Databáze: | OpenAIRE |
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