On the property M conjecture for the Heisenberg Lie algebra

Phil Hanlon, Michelle L Galloway

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)219-231
Number of pages13
JournalJournal of Combinatorial Theory, Series A
Volume99
Issue number2
DOIs
StatePublished - 2002

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Heisenberg Algebra
Algebra
Homology
Lie Algebra
Cohomology
Express
Three-dimensional

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.

In: Journal of Combinatorial Theory, Series A, Vol. 99, No. 2, 2002, p. 219-231.

Research output: Contribution to journalArticle

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