The Ricci curvature of finite dimensional approximations to loop and path groups

Let W(G) and C(G) denote the path and loop groups respectively of a connected real unimodular Lie group G endowed with a left-invariant Riemannian metric. We study the Ricci curvature of certain finite dimensional approximations to these groups based on partitions of the interval vertical bar 0, 1 vertical bar. We find that the Ricci curvatures of the finite dimensional approximations are bounded below independent of partition iff G is of compact type with an Ad-invariant metric. (C) 2008 Elsevier Masson SAS. All rights reserved.