Completable two step nilpotent Lie algebras of type (2, p)

摘要

A Lie algebra is called complete if its centre is zero and all its derivations are inner. A nilpotent Lie algebra is called completable if it is the maximal nilpotent ideal of a complete solvable Lie algebra. A two-step nilpotent Lie algebra N is said to be of type (2 , p) , if dim N = p + 2 and dim [ N , N ] = 2. In this paper, based on the classification result of M. Gauger, we classify two step completable complex nilpotent Lie algebras of type (2 , p) .