Infinite dimensional Riemannian symmetric spaces with fixed-sign curvature operator

Bruno Duchesne (1, 2)

1 Einstein Institute of Mathematics
2 IECL - Institut Élie Cartan de Lorraine

We associate to any Riemannian symmetric space (of finite or infinite dimension) a L$^*$-algebra, under the assumption that the curvature operator has a fixed sign. L$^*$-algebras are Lie algebras with a pleasant Hilbert space structure. The L$^*$-algebra that we construct is a complete local isomorphism invariant and allows us to classify Riemannian symmetric spaces with fixed-sign curvature operator. The case of nonpositive curvature is emphasized.

Mots clés: L*-algebras; Riemannian symmetric spaces

Domaines: Géométrie différentielle [math.DG]; Mathématiques générales [math.GM]

Bruno Duchesne. Infinite dimensional Riemannian symmetric spaces with fixed-sign curvature operator. Annales de l'Institut Fourier, 2015, 65 (1), pp.211-244. ⟨10.5802/aif.2929⟩. ⟨hal-00680969v3⟩