Six-dimensional nilpotent Lie algebras
By Serena Cicalò, W. D. Graaf, Csaba Schneider. 2010
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Abstract We give a full classification of six-dimensional nilpotent Lie algebras over an arbitrary field, including fields that are not algebraically closed and fields of characteristic 2. To achieve the classification we use the action of the automorphism group on the second cohomology space, as isomorphism types of nilpotent Lie algebras correspond to orbits of subspaces under this action. In some cases, these orbits are determined using geometric invariants, such as the Gram determinant or the Arf invariant. As a byproduct, we completely determine, for a four-dimensional vector space V , the orbits of GL ( V ) on the set of two-dimensional subspaces of V ∧ V .
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6fbddc00a65ab954b0d73a1749a3759ad335142f
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In Algebra and Number Theory
In Mathematical Physics
Citations in the corpus
- Degenerations of nilpotent algebras (2019, background): “One can also look at the classification of 4-dimensional nilpotent associative algebras [19], 4-dimensional nilpotent Novikov algebras [37], 4-dimensional nilpotent bicommutative algebras [39], 5-dimensional nilpotent restricted Lie agebras [17], 5-dimensional nilpotent Jordan algebras [30], 6-dimen”