Semigroups generated by cosets and characteristics functions of semigroups / Semigrupos gerados por classes laterais e funções caracteristicas de semigrupos
AUTOR(ES)
Laercio Jose dos Santos
DATA DE PUBLICAÇÃO
2007
RESUMO
This work is made of two parts. In the first one, we gave necessary and sufficient conditions for a family of cosets of a Lie subgroup to generate a subsemigroup with nonempty interior. We apply these conditions to symmetric pairs where the group is semi-simple. As a consequence we prove that for several involutive automorphisms the fixed points subgroup is a maximal semigroup. In the second part, we define a characteristic function of a subsemigroup of a semi- simple Lie group and we find a subset where the function is defined. This is made through general theory of semigroups in semi-simple groups. The characteristic function is used, together with some additional hypothesis, for to create a Riemannian metric in the orbits of the unity subgroup of the semigroup. With this metric we gave a necessary condition for a subgroup be embedded in a proper semigroup with nonempty interior
ASSUNTO(S)
algebras de homogeneous spaces semigroups lie espaços homogeneos lie groups semigrupos lie lie algebras grupos de espaços simetricos symmetric spaces
