Deformations of the nilpotent infinite-dimensional Lie algebra \(L_ 2\) (Q1320688)

Let \(W\) be the Witt algebra over \(\mathbb{C}\) with base \(\{e_ i\}\), \(i\geq - 1\), such that \([e_ i,e_ j]= (j- i)e_{i+j}\) and \(L_ k\), \(k\geq 1\), a subalgebra of \(W\) with base \(\{e_ k,e_{k+1},\dots\}\). The authors study deformations of \(L_ 2\) and determine \(H^ 2(L_ 2,L_ 2)\).