On the Betti Numbers of Nilpotent Lie Algebras of Small Dimension

On the cohomology of a class of nilpotent Lie algebras

“…For all nilpotent Lie algebras L of dimension ^ 7, the sequence {^(.L)}^^ is unimodal, see for instance [4]. However unimodality is not a property shared by nilpotent Lie algebras in general, see for instance [2].…”

Determination of 7-Dimensional Indecomposable Nilpotent Complex Lie Algebras by Adjoining a Derivation to 6-Dimensional Lie Algebras

“…Now τ 1 , τ 2 generate S 3 and s 1 , s 2 generate G ∼ = S 3 . It follows that there exists an isomorphism f : 3.1(iλ) ). In particular, the cases λ = 0, λ = 1 are isomorphic, and so are the 3 cases λ = −1, λ = 2, λ = 1 2 .…”

“…Adjoint and trivial cohomologies for all complex 7-dimensional indecomposable NLAs, along with their weight systems under the action of the maximal torus of g have been computed in [17] (see also [15,18], and for trivial cohomology [3]). It is a fact that, for the Lie algebras under consideration, the trivial cohomology is ineffective in separating nonisomorphic Lie algebras and doesn't refine the classification by weight systems of the algebras.…”

Adjoint and Trivial Cohomologies of Nilpotent Complex Lie Algebras of Dimension ≤7

“…The results appear as in Tables 3,4,5,6,7,8,9,10,11,12,13. For continuous series, the places where gaps occur for the singular values are underlined.…”