A computer-based approach to the classification of nilpotent Lie algebras. (English) Zbl 1093.17004

Schneider, Csaba

Exp. Math. 14, No. 2, 153-160 (2005).

Adapting E. A. O’Brien’s \(p\)-group generation algorithm [J. Symb. Comput. 9, 677–698 (1990; Zbl 0736.20001)] to nilpotent Lie algebras, the author finds the number of isomorphism types of six- and seven-dimensional nilpotent Lie algebras over fields with 2, 3 and 5 elements. He also finds the number of isomorphism types of nilpotent Lie algebras of dimension eight and nine over the field with 2 elements.

Reviewer: Ernest L. Stitzinger (Raleigh)

MSC:

17B05	Structure theory for Lie algebras and superalgebras
17B30	Solvable, nilpotent (super)algebras

Keywords:

\(p\)-group generation algorithm

Citations:

Zbl 0736.20001

Software:

GAP; Sophus