On the Betti Numbers of Nilpotent Lie Algebras of Small Dimension

  • Grant Cairns
  • Barry Jessup
  • Jane Pitkethly
Part of the Progress in Mathematics book series (PM, volume 145)


The work of Golod and Šafarevič on class field towers motivated the conjecture that b2 > b2 1/4 for nilpotent Lie algebras of dimension at least 3, where b i denotes the i th Betti number. Using a new lower bound for b 2 and a characterization of Lie algebras of the form g/Z(g), we prove this conjecture for 2-step algebras. We also give the Betti numbers of nilpotent Lie algebras of dimension at most 7 and use them to establish the conjecture for all nilpotent Lie algebras whose centres have codimension ≤ 7.


Betti Number Riemannian Foliation Dense Leaf Abelian Ideal Maximal Abelian Subalgebra 
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Copyright information

© Birkhäuser Boston 1997

Authors and Affiliations

  • Grant Cairns
    • 1
  • Barry Jessup
    • 2
  • Jane Pitkethly
    • 3
  1. 1.School of MathematicsLa Trobe UniversityMelbourneAustralia
  2. 2.Department of MathematicsUniversity of OttawaOttawaCanada
  3. 3.School of MathematicsLa Trobe UniversityMelbourneAustralia

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