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Archiv der Mathematik

, Volume 77, Issue 2, pp 177–180 | Cite as

The mod 4 behaviour of total Lie algebra cohomology

  • G. Cairns
  • G. Kim
  • 34 Downloads

Abstract.

We show that if L is a unimodular Lie algebra over a field of characteristic \(\ne 2\), then the dimension \(\sigma\)(L) of the total cohomology of L is a multiple of 4 when \(\dim(L)\not\equiv 3\) (mod 4). However, contrary to a claim by Deninger and Singhof, we give an example of a rational nilpotent algebra L of dimension 15 with \(\sigma(L)\not\equiv 0\) (mod 4). Over fields of characteristic 2, we completely classify those algebras L with \(\sigma(L)\not\equiv 0\) (mod 4).

Keywords

Algebra Cohomology Nilpotent Algebra Total Cohomology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 2001

Authors and Affiliations

  • G. Cairns
    • 1
  • G. Kim
    • 1
  1. 1.School of Mathematics, La Trobe University, Melbourne, Australia 3083AU

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