Infinite dimensional Riemannian symmetric spaces with fixed-sign curvature operator

Abstract

We associate to any Riemannian symmetric space (of finite or infinite dimension) a L${}^{\ast }$-algebra, under the assumption that the curvature operator has a fixed sign. L${}^{\ast }$-algebras are Lie algebras with a pleasant Hilbert space structure. The L${}^{\ast }$-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.

arXiv commentA paraître aux annales de l'institut Fourier

Cited by in corpus (3)

• Geometry and dynamics in Gromov hyperbolic metric spaces: With an emphasis on non-proper settings
• Furstenberg Maps For CAT(0) Targets Of Finite Telescopic Dimension
• Representations of infinite dimension orthogonal groups of quadratic forms with finite index