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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75492We 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 $-\infty$.Differential GeometryMathematical Physics58B20, 81R10Hilbert-Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometrytext