Betti Number Behavior for Nilpotent Lie Algebras

被引：0
作者：
Hannes Pouseele
机构：
[1] Katholieke Universiteit Leuven Campus Kortrijk,Department of Mathematics
来源：
Geometriae Dedicata | 2006年 / 122卷
关键词：
Lie algebra; cohomology; Betti numbers; 17B56;
D O I：
暂无
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学科分类号：
摘要：
We discuss three general problems concerning the cohomology of a (real or complex) nilpotent Lie algebra: first of all, determining the Betti numbers exactly; second, determining the distribution these Betti numbers follow; and finally, estimating the size of the individual cohomology spaces or the total cohomology space. We show how spectral sequence arguments can contribute to a solution in a concrete setting. For one-dimensional extensions of a Heisenberg algebra, we determine the Betti numbers exactly. We then show that some families in this class have a M-shaped Betti number distribution, and construct the first examples with an even more exotic Betti number distribution. Finally, we discuss the construction of (co)homology classes for split metabelian Lie algebras, thus proving the Toral Rank Conjecture for this class of algebras.
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页码：77 / 88
页数：11
相关论文
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