Journal of Lie Theory

no. 2
A Converse to the Second Whitehead Lemma
Journal of Lie Theory, Volume 18 (2008) no. 2, pp. 295-299
In this paper we state and prove the following version of a converse to the Second Whitehead Lemma: A finite-dimensional Lie algebra over a field of characteristic zero with vanishing second cohomology in any finite-dimensional module must be one of the following: (i) a one-dimensional algebra; (ii) a semisimple algebra; (iii) the direct sum of a semisimple algebra and a one-dimensional algebra.
DOI: 10.5802/jolt.495
Classification: 17B56
Keywords: Second Whitehead Lemma 
@article{JOLT_2008_18_2_a2,
     author = {P. Zusmanovich},
     title = {A {Converse} to the {Second} {Whitehead} {Lemma}},
     journal = {Journal of Lie Theory},
     pages = {295--299},
     year = {2008},
     volume = {18},
     number = {2},
     doi = {10.5802/jolt.495},
     zbl = {1163.17023},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.495/}
}
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P. Zusmanovich. A Converse to the Second Whitehead Lemma. Journal of Lie Theory, Volume 18 (2008) no. 2, pp. 295-299. doi: 10.5802/jolt.495

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