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

Qifen Jiang; Ran Shen; Yucai Su

paper

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

arXiv:math/0608406

Abstract

It is known that the second Leibniz homology group $H L_{2} (s t l_{n} (R))$ of the Steinberg Leibniz algebra $s t l_{n} (R)$ is trivial for $n \geq 5$ . In this paper, we determine $H L_{2} (s t l_{n} (R))$ explicitly (which are shown to be not necessarily trivial) for $n = 3, 4$ without any assumption on the base ring.

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