Hilbert-schmidt Groups as Infinite-dimensional Lie Groups and Their Riemannian Geometry
نویسنده
چکیده
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 −∞. Table of
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