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Journal of Lie Theory, Vol. 10, No. 2, pp. 435-441 (2000)
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Lie Algebras of Least Cohomology

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Grant Cairns and Gunky Kim

School of Mathematics

La Trobe University

Melbourne, Australia 3083

G.Cairns@latrobe.edu.au

G.Kim@latrobe.edu.au

**Abstract:** We classify those finite dimensional Lie algebras, over a field $\k$ of characteristic zero, whose cohomology with trivial coefficients has dimension 2. We show that the only such algebras are the 3-dimensional simple algebras and the semi-direct products $\n\rtimes_\phi \k$, where $\n$ is a nilpotent Lie algebra and $\phi\colon\n\to \n$ is a derivation which induces a non-singular map in each cohomology space $H^i(\n)$, for $i>0$.

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