Minimal and maximal semigroups related to causal symmetric spaces

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Let G/H be an irreducible globally hyperbolic semisimple symmetric space, and let S ⊆ G be a subsemigroup containing H not isolated in S. We show that if S° ≠ Ø then there are H -invariant minimal and maximal cones Cmin ⊆ Cmax in the tangent space at the origin such that H exp Cmin ⊆ S ⊆ HZK (a) exp Cmax. A double coset decomposition of the group G in terms of Cartan subspaces and the group H is proved. We also discuss the case where G/H is of Cayley type.

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Semigroup Forum

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