On the property M conjecture for the Heisenberg Lie algebra

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]/(tk+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 3k+1 by constructing a simple basis for cohomology. © 2002 Elsevier Science (USA).