
Journal of Lie Theory 27 (2017), No. 4, 11411150 Copyright Heldermann Verlag 2017 Reconstruction from Representations: Jacobi via Cohomology Boris Kruglikov Dept. of Mathematics and Statistics, Faculty of Science and Technology, UiT the Arctic University of Norway, Tromsoe 9037, Norway boris.kruglikov@uit.no Henrik Winther Dept. of Mathematics and Statistics, Faculty of Science and Technology, UiT the Arctic University of Norway, Tromsoe 9037, Norway henrik.winther@uit.no A subalgebra h of a Lie algebra g determines an hrepresentation ρ on m = g / h. We discuss how to reconstruct g from (h, m, ρ). In other words, we find all the ingredients for building nonreductive Klein geometries. The Lie algebra cohomology plays a decisive role here. Keywords: Homogeneous space, Lie algebra cohomology, nonreductive isotropy. MSC: 17B55, 22E47, 17B05, 22F30 [ Fulltextpdf (285 KB)] for subscribers only. 