### 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.

Original language | English (US) |
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Pages (from-to) | 219-231 |

Number of pages | 13 |

Journal | Journal of Combinatorial Theory. Series A |

Volume | 99 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2002 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

Hanlon, P., & Wachs, M. L. (2002). On the property M conjecture for the Heisenberg Lie algebra.

*Journal of Combinatorial Theory. Series A*,*99*(2), 219-231. https://doi.org/10.1006/jcta.2002.3258