### 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) |
---|---|

Pages (from-to) | 219-231 |

Number of pages | 13 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 99 |

Issue number | 2 |

DOIs | |

State | Published - 2002 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

**On the property M conjecture for the Heisenberg Lie algebra.** / Hanlon, Phil; Galloway, Michelle L.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory, Series A*, vol. 99, no. 2, pp. 219-231. https://doi.org/10.1006/jcta.2002.3258

}

TY - JOUR

T1 - On the property M conjecture for the Heisenberg Lie algebra

AU - Hanlon, Phil

AU - Galloway, Michelle L

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0036050231&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036050231&partnerID=8YFLogxK

U2 - 10.1006/jcta.2002.3258

DO - 10.1006/jcta.2002.3258

M3 - Article

VL - 99

SP - 219

EP - 231

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 2

ER -