# Solvable extensions of a special class of nilpotent Lie algebras

## A. Shabanskaya and G. Thompson

Address:

Corresponding author: Department of Mathematics and Computer Science, Eastern Connecticut State University, 83 Windham Street, Willimantic, CT 06226, USA

Department of Mathematics and Statistics, The University of Toledo, 2801 W Bancroft St. Toledo, OH 43606, USA

E-mail: gerard.thompson@utoledo.edu

Abstract: A pair of sequences of nilpotent Lie algebras denoted by $N_{n,11}$ and $N_{n,19}$ are introduced. Here $n$ denotes the dimension of the algebras that are defined for $n\ge 6$; the first term in the sequences are denoted by $6.11$ and $6.19$, respectively, in the standard list of six-dimensional Lie algebras. For each of $N_{n,11}$ and $N_{n,19}$ all possible solvable extensions are constructed so that $N_{n,11}$ and $N_{n,19}$ serve as the nilradical of the corresponding solvable algebras. The construction continues Winternitz' and colleagues' program of investigating solvable Lie algebras using special properties rather than trying to extend one dimension at a time.

AMSclassification: primary 17B30; secondary 17B40, 17B05.

Keywords: solvable Lie algebra, nilradical, derivation.

DOI: 10.5817/AM2013-3-141