A counterexample to a Proposition of Feldvoss-Wagemann and Burde-Wagemann

Abstract

Our (weak) conjecture claims that a finite dimensional Lie algebra $\mathbf{g}$ over the field of complex numbers is semi-simple iff the Leibniz homology vanishes in positive dimensions $H{L}_i(\mathbf{g})=0$, $i>0$. We will indicate a mistake in the recent proof of this conjecture due to Burde and Wagemann.