The multiplier and the cover of direct sums of Lie algebras (Q2920391)

The authors obtain an analog to the group theory result of \textit{C. Miller} [Proc. Am. Math. Soc. 3, 588--595 (1952; Zbl 0047.25703)] when they show the the Schur multiplier of the direct sum of two Lie algebras is the direct sum of the multipliers of the factors and the tensor product of the factors. In the finite dimensional case, the result was shown by \textit{P. Batten, K. Moneyhun} and the reviewer [Commun. Algebra 24, No. 14, 4319--4330 (1996; Zbl 0893.17008)]. They also obtain that the cover for the direct sum of two Lie algebras is the direct sum of the covers of the factors and the tensor product of the covers of the factors.