Central Extensions of Steinberg Lie Superalgebras of Small Rank

Abstract

It was shown by Mikhalev and Pinchuk (2000) that the second homology group H ₂(𝔰𝔱(m,n,R)) of the Steinberg Lie superalgebra 𝔰𝔱(m,n,R) is trivial for m + n ≥ 5. In this article, we will work out H ₂(𝔰𝔱(m,n,R)) explicitly for m + n = 3, 4.

Key Words:

• Central extensions
• Steinberg Lie superalgebras

2000 Mathematics Subject Classification:

• 17B55
• 17B60

ACKNOWLEDGMENT

We would like to thank the referee for many helpful suggestions which improved the exposition of this article.

Research of the third author was partially supported by NSERC of Canada and Chinese Academy of Science.

Notes

Communicated by K. C. Misra.