Journal of Lie Theory

no. 4
A Converse to the Whitehead Theorem
Journal of Lie Theory, Volume 18 (2008) no. 4, pp. 811-815
In this postscript to our earlier note [ J. Lie Theory 18 (2008) 295--299] we show that finite-dimensional Lie algebras over a field of characteristic zero such that their high-degree cohomology in any finite-dimensional non-trivial irreducible module vanishes, are, essentially, direct sums of semisimple and nilpotent algebras.
DOI: 10.5802/jolt.526
Classification: 17B56
Keywords: Whitehead theorem, cohomology groups of Lie algebras 
@article{JOLT_2008_18_4_a3,
     author = {P. Zusmanovich},
     title = {A {Converse} to the {Whitehead} {Theorem}},
     journal = {Journal of Lie Theory},
     pages = {811--815},
     year = {2008},
     volume = {18},
     number = {4},
     doi = {10.5802/jolt.526},
     zbl = {1169.17012},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.526/}
}
TY  - JOUR
AU  - P. Zusmanovich
TI  - A Converse to the Whitehead Theorem
JO  - Journal of Lie Theory
PY  - 2008
SP  - 811
EP  - 815
VL  - 18
IS  - 4
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.526/
DO  - 10.5802/jolt.526
ID  - JOLT_2008_18_4_a3
ER  - 
%0 Journal Article
%A P. Zusmanovich
%T A Converse to the Whitehead Theorem
%J Journal of Lie Theory
%D 2008
%P 811-815
%V 18
%N 4
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.526/
%R 10.5802/jolt.526
%F JOLT_2008_18_4_a3
P. Zusmanovich. A Converse to the Whitehead Theorem. Journal of Lie Theory, Volume 18 (2008) no. 4, pp. 811-815. doi: 10.5802/jolt.526

Cited by Sources: