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Free submodules for the central representation in the cohomology of Lie algebras
Author(s):
Grant
Cairns;
Barry
Jessup
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1919-1923.
MSC (2000):
Primary 17B55, 17B56;
Secondary 55P62
Posted:
February 7, 2008
MathSciNet review:
2383497
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Abstract:
If  is the centre of the Lie algebra  , its cohomology  is naturally a module over the exterior algebra  . Under suitable hypotheses on  , motivated by recent work by Pouseele and Tirao, we find free summands in  for this module structure, thus establishing the Toral Rank Conjecture for a new class of Lie algebras.
References:
-
- 1.
- Grant Cairns and Barry Jessup, New bounds on the Betti numbers of nilpotent Lie algebras, Comm. Algebra 25 (1997), no. 2, 415-430. MR 1428787 (98a:17032)
- 2.
- -, Cohomology operations for Lie algebras, Trans. Amer. Math. Soc. 356 (2004), no. 4, 1569-1583 (electronic). MR 2034319 (2005a:17018)
- 3.
- Ch. Deninger and W. Singhof, On the cohomology of nilpotent Lie algebras, Bull. Soc. Math. France 116 (1988), no. 1, 3-14. MR 946276 (90c:17023)
- 4.
- Stephen Halperin, Le complexe de Koszul en algèbre et topologie, Ann. Inst. Fourier (Grenoble) 37 (1987), no. 4, 77-97. MR 927392 (89d:55040)
- 5.
- Hannes Pouseele and Paulo Tirao, Constructing Lie algebra homology classes, J. Algebra 292 (2005), no. 2, 585-591. MR 2172169 (2006h:17028)
- 6.
- Paulo Tirao, A refinement of the toral rank conjecture for
 -step nilpotent Lie algebras, Proc. Amer. Math. Soc. 128 (2000), no. 10, 2875-2878. MR 1664387 (2000m:17026) - 7.
- -, On the homology of graded Lie algebras, J. Pure Appl. Algebra 156 (2001), no. 2-3, 357-366. MR 1808831 (2001m:17026)
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Additional Information:
Grant
Cairns
Affiliation:
Department of Mathematics, La Trobe University, Melbourne, Australia 3086
Email:
G.Cairns@latrobe.edu.au
Barry
Jessup
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada K1N6N5
Email:
bjessup@uottawa.ca
DOI:
10.1090/S0002-9939-08-09250-2
PII:
S 0002-9939(08)09250-2
Received by editor(s):
October 25, 2006
Posted:
February 7, 2008
Additional Notes:
This research was supported in part by NSERC and the ARC
The second author would like to thank the members of the Department of Mathematics and Statistics at La Trobe University for their hospitality during his stay there
Communicated by:
Paul Goerss
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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