Bounds for the dimension of the center factor in capable nilpotent Lie algebras of class two

Abstract

Let L be a finite-dimensional nilpotent Lie algebra of class two over a field $\mathbb{F}$ of characteristic different from two. The aim of the present paper is to give an upper bound for the dimension of the center factor L/Z(L) of a capable Lie algebra L. As a result, we also find a lower bound for the dimension of the derived subalgebra L² for a capable Lie algebra L. Furthermore, we also give some criteria for determining the capability of L.

Keywords:

• Capability
• nilpotent lie algebra of class two

Mathematics Subject Classification 2010:

• 17B30
• 17B05
• 17B99

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The author was supported by the postdoctoral grant ‘CAPES/PRINT-Edital $n^{\circ }41/2017$, Process number: 88887.364925/2019-00,’ at the Federal University of Minas Gerais.