Classification of Nilpotent Lie Algebras of Dimension 7 (Over Algebraically Closed Fields and R)

This PhD thesis is concerned with the classification of 7-dimensional nilpotent Lie algebras. Skjelbred and Sund have published in 1977 their method of constructing all nilpotent Lie algebras of dimension n given those algebras of dimension < n, and their automorphism groups. By using this method, we construct all nonisomorphic 7-dimensional nilpotent Lie algebras in the following two cases: (1) over an
algebraically closed field of arbitrary characteristic except 2; (2) over the real field R.
We have compared our lists with three of the most recent lists (those of Seeley, Ancochea-Goze, and Romdhani). While our list in case (1) over C differs greatly from that of Ancochea-Goze, which contains too many errors to be usable, it agrees with that of Seeley apart from a few corrections that should be made in his list,
Our list in case (2) over R contains all the algebras on Romdhani's list, which omits many algebras.