Semi-groupe de Lie associé à une algèbre de Jordan euclidienne

Abstract : To any formal real Jordan algebra one may attach a symmetric cone. We choose to tudy the sub-semigroup of elements of the conformal group which preserves the cone. We give two additional characterizations of this semigroup. The first characterization realizes the semigroup as the real points of the OL'SHANSKII characterization concerns the symmetric space of Carley type attached to the Jordan algebra. This latter space imbeds in the pruduct of two copies of the Silov boundary of the bounded symmetric domain and we explicitly describe the image of this imbedding. This space is causal and we proove that the causal structure is global and the semigroup associated to the corresponding order is precisely the semigroup that we introduce. In addition to these characterizations, we also obtain two decomposition of this semigroup. The first decomposition is the "HARISH-CHANDRA" decomposition and we use it to proove that the semigroup is a semigroup is a semigroup of contraction with respect to the invariant Riemannian structure to the cone. The second decomposition is the so-called OL'SHANSKII decomposition.
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Khalid Koufany. Semi-groupe de Lie associé à une algèbre de Jordan euclidienne. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 1993. Français. ⟨NNT : 1993NAN10172⟩. ⟨tel-01748609⟩

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