Nilpotent lie algebras with a small second derived quotient [electronic resource] /

by Zack, Laurie Margaret

ZACK, LAURIE. Nilpotent Lie Algebras with a Small Second Derived Quotient. (Under the direction of Ernie L. Stitzinger.) There are many parallels between groups and Lie algebras, and mathematicians have been studying the similarities between them for decades. Many times researchers can look at results from group theory and translate them over into results in Lie algebras and vice versa. In 2003, Csaba Schneider published a paper in the Journal of Algebra about finite p-groups G, with the properties G?? ?= 1 and |G?/G??| = p3. Schneider used Lie algebra calculations to inspire the ideas behind the group structure when G is generated by two elements. He then extended the group ideas to find the structure of G when generated by more than two elements and stated that it would be interesting to look at these results in Lie algebras. This paper completes the analogous Lie algebra problem, when L is a nilpotent Lie algebra with properties dim(L?/L??) = 3 and L?? ?= 0. In this paper, not only have we found all the Lie algebra analogues to Schneider’s results, we have also classified these algebras over the complex numbers.