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 ≥ 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.

Key Words:

• Homology group
• Leibniz algebra
• The Steinberg Leibniz algebra

2000 Mathematics Subject Classification:

• 17A32
• 17B55
• 17B60

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.