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 ≥ 5. In this article, 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.
ACKNOWLEDGMENT
This work is supported by NSF grants 10871125, 10471091 of China and “One Hundred Talents Program” from University of Science and Technology of China.
Notes
Communicated by K. C. Misra.