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

Qifen Jiang·Ran Shen·Yucai Su
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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.

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Qifen Jiang, Ran Shen, Yucai Su. 2009-11-24. Second homology groups and universal coverings of Steinberg Leibniz algebras of small characteristic. https://arxiv.org/abs/math/0608406

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