Leibniz Central Extension on a Block Lie Algebra

Abstract

Let [Formula: see text] be the Lie algebra over C with basis {L m,n | m,n ∈ Z, n ≥ 0} and relations [L m,n ,L m 1 ,n 1 ] =((n+1)m 1 -(n 1 +1)m) L m+m 1 ,n+n 1 . In this paper, we determine the second cohomology group and the second Leibniz cohomology group of [Formula: see text].