Infinite dimensional Riemannian symmetric spaces with fixed-sign curvature operator

Details Infinite dimensional Riemannian symmetric spaces with fixed-sign curvature operator Infinite dimensional Riemannian symmetric spaces with fixed-sign curvature operator

2012-04-26

arxiv.org/abs/1204.6012v1

Mathematics

Differential Geometry

25 pages

Scientific paper

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

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