We introduce the notion of compatible actions in the context of split extensions of Lie algebras over a field k. Using compatible actions, we construct new resolutions to compute the cohomology of semi-direct products of Lie algebras and give an alternative way to construct the Hochschild-Serre spectral sequence associated to a split extension. Finally, we describe several instances in which this spectral sequence collapses at the second page and obtain a sharper bound for its length in the finite dimensional case.
Dieter Degrijse; Nansen Petrosyan. On the Cohomology of Split Lie Algebra Extensions. Journal of Lie Theory, Tome 22 (2012) no. 1, pp. 1-15. http://geodesic.mathdoc.fr/item/JOLT_2012_22_1_a0/
@article{JOLT_2012_22_1_a0,
author = {Dieter Degrijse and Nansen Petrosyan},
title = {On the {Cohomology} of {Split} {Lie} {Algebra} {Extensions}},
journal = {Journal of Lie Theory},
pages = {1--15},
year = {2012},
volume = {22},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2012_22_1_a0/}
}
TY - JOUR
AU - Dieter Degrijse
AU - Nansen Petrosyan
TI - On the Cohomology of Split Lie Algebra Extensions
JO - Journal of Lie Theory
PY - 2012
SP - 1
EP - 15
VL - 22
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2012_22_1_a0/
ID - JOLT_2012_22_1_a0
ER -
%0 Journal Article
%A Dieter Degrijse
%A Nansen Petrosyan
%T On the Cohomology of Split Lie Algebra Extensions
%J Journal of Lie Theory
%D 2012
%P 1-15
%V 22
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2012_22_1_a0/
%F JOLT_2012_22_1_a0
