Abstract
We prove a fundamental case of a conjecture of the first author which expresses the homology of the extension of the Heisenberg Lie algebra by
C
[
t]/(
t
k+1
) in terms of the homology of the Heisenberg Lie algebra itself. More specifically, we show that both the 0th and (
k+1)th
x-graded components of homology of this extension of the three-dimensional Heisenberg Lie algebra have dimension 3
k+1
by constructing a simple basis for cohomology.
