Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2

Nilpotent 6-dimensional Lie algebras over any field of characteristic not 2 are classified. The proof of this classification is essentially constructive: for a given 6-dimensional nilpotent Lie algebra L, following the steps of the proof, it is possible to find a Lie algebra M that occurs in the classification, and an isomorphism L→M. In the proof a method due to Skjelbred and Sund is used, along with a method based on Gröbner bases to find isomorphisms.