The mod 4 behaviour of total Lie algebra cohomology
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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).
KeywordsAlgebra Cohomology Nilpotent Algebra Total Cohomology
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