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 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.
In: Journal of Combinatorial Theory, Series A, Vol. 99, No. 2, 2002, p. 219-231.Research output: Contribution to journal › Article
}
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 -