Nilpotent Lie Algebras with a Small Second Derived Quotient¹

¹Dissertation results.

Abstract

Here we find the structure of nilpotent Lie algebras L with dim(L′/L″) = 3 and L″ ≠ 0. Following the pattern of results of Csaba Schneider in p-groups, we show that L is the central direct sum of ideals H and U, where U is the direct sum of a generalized Heisenberg Lie algebra and an abelian Lie algebra. We then find over the complex numbers that H falls into one of fourteen isomorphism classes.

Key Words:

• Nilpotent Lie algebra
• Second derived quotient

2000 Mathematics Subject Classification:

• 17B30

Notes

Communicated by K. C. Misra.

¹Dissertation results.