Second homology groups and universal coverings of Steinberg Leibniz algebras of small characteristic

Abstract

It is known that the second Leibniz homology group $HL_2(stl_n(R))$ of the Steinberg Leibniz algebra $stl_n(R)$ is trivial for $n\geq 5$. In this paper, we determine $HL_2(stl_n(R))$ explicitly (which are shown to be not necessarily trivial) for $n=3, 4$ without any assumption on the base ring.