Leibniz homology of unitary Lie algebras (Q1300651)

The author studies the second Leibniz homology group \(HL_2\) of the elementary unitary Lie algebras \(en_n(R,-,\gamma)\) and \(eu(\dot{g};R,-)\), where \((R,-)\) is an associative involutive algebra and \(\dot{g}\) a finite dimensional split Lie algebra. Then some consequences are derived. In particular, the result due to \textit{J.-L. Loday} and \textit{T. Pirashvili} [Math. Ann. 296, 139-158 (1993; Zbl 0821.17022)] on \(HL_2\) of the Lie algebras \(sl_n(S)\) and \(st_n(S)\), where \(S\) is an associative algebra, is recovered.