On the property M conjecture for the Heisenberg Lie algebra

[摘要] 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. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-08-01