Journal of Lie Theory 27 (2017), No. 4, 1141--1150
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 90-37, Norway
boris.kruglikov@uit.no
Henrik Winther
Dept. of Mathematics and Statistics, Faculty of Science and Technology, UiT the Arctic University of Norway, Tromsoe 90-37, Norway
henrik.winther@uit.no
A subalgebra h of a Lie algebra g determines an h-representation 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 non-reductive Klein geometries. The Lie algebra cohomology plays a decisive role here.
Keywords: Homogeneous space, Lie algebra cohomology, non-reductive isotropy.
MSC: 17B55, 22E47, 17B05, 22F30
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