Minimal and Maximal Semigroups Related to Causal Symmetric Spaces |
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Authors: | Andreas Neumann Gestur Ólafsson |
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Abstract: | Let G/H be an irreducible globally hyperbolic semisimple symmetric space, and let S ³ G be a subsemigroup containing H not isolated in S. We show that if So p 0 then there are H-invariant minimal and maximal cones Cmin ³ Cmax in the tangent space at the origin such that H exp Cmin ³ S ³ HZK(a)expCmax. 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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