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The cohomology of the Heisenberg Lie algebras over fields of finite characteristic
Author(s):
Grant
Cairns;
Sebastian
Jambor
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3803-3807.
MSC (2000):
Primary 17B55, 17B56
Posted:
May 22, 2008
MathSciNet review:
2425718
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Abstract:
We give explicit formulas for the cohomology of the Heisenberg Lie algebras over fields of finite characteristic. We use this to show that in characteristic two, unlike all other cases, the Betti numbers are unimodal.
References:
-
- 1.
- Grant F. Armstrong, Unimodal Betti numbers for a class of nilpotent Lie algebras, Comm. Algebra 25 (1997), no. 6, 1893-1915. MR 1446138 (98e:17031)
- 2.
- Grant F. Armstrong, Grant Cairns, and Barry Jessup, Explicit Betti numbers for a family of nilpotent Lie algebras, Proc. Amer. Math. Soc. 125 (1997), no. 2, 381-385. MR 1353371 (97d:17013)
- 3.
- Hannes Pouseele, On the cohomology of extensions by a Heisenberg Lie algebra, Bull. Austral. Math. Soc. 71 (2005), no. 3, 459-470. MR 2150935 (2006c:17028)
- 4.
- L. J. Santharoubane, Cohomology of Heisenberg Lie algebras, Proc. Amer. Math. Soc. 87 (1983), no. 1, 23-28. MR 677223 (84b:17010)
- 5.
- Emil Sköldberg, The homology of Heisenberg Lie algebras over fields of characteristic two, Math. Proc. R. Ir. Acad. 105A (2005), no. 2, 47-49 (electronic). MR 2164586
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Additional Information:
Grant
Cairns
Affiliation:
Department of Mathematics, La Trobe University, Melbourne, Australia 3086
Email:
G.Cairns@latrobe.edu.au
Sebastian
Jambor
Affiliation:
Department of Mathematics, La Trobe University, Melbourne, Australia 3086
Email:
Sebastian@momo.math.rwth-aachen.de
DOI:
10.1090/S0002-9939-08-09422-7
PII:
S 0002-9939(08)09422-7
Received by editor(s):
November 6, 2006,
Received by editor(s) in revised form:
September 23, 2007
Posted:
May 22, 2008
Communicated by:
Dan M. Barbasch
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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