On the property M conjecture for the Heisenberg Lie algebra

Phil Hanlon; Michelle L. Wachs

doi:10.1006/jcta.2002.3258

On the property M conjecture for the Heisenberg Lie algebra

Phil Hanlon, Michelle L. Wachs

Mathematics

Research output: Contribution to journal › Article

3 Scopus citations

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	https://doi.org/10.1006/jcta.2002.3258
State	Published - Jan 1 2002

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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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

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