Hilbert-Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometry

Details Hilbert-Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometry Hilbert-Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometry

2005-06-14

arxiv.org/abs/math/0506276v1

Mathematics

Differential Geometry

Scientific paper

We describe the exponential map from an infinite-dimensional Lie algebra to an infinite-dimensional group of operators on a Hilbert space. Notions of differential geometry are introduced for these groups. In particular, the Ricci curvature, which is understood as the limit of the Ricci curvature of finite-dimensional groups, is calculated. We show that for some of these groups the Ricci curvature is $-\infty$.

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