On classification of (n + 6)-dimensional nilpotent n-Lie algebras of class 2 with n ≥ 4

Abstract

Purpose – The purpose of this paper is to determine the structure of nilpotent (n+6)-dimensional n-Lie algebras of class 2 when n≥4. Design/methodology/approach – By dividing a nilpotent (n+6)-dimensional n-Lie algebra of class 2 by a central element, the authors arrive to a nilpotent (n+5) dimensional n-Lie algebra of class 2. Given that the authors have the structure of nilpotent (n+5)-dimensional n-Lie algebras of class 2, the authors have access to the structure of the desired algebras. Findings – In this paper, for each n≥4, the authors have found 24 nilpotent (n+6) dimensional n-Lie algebras of class 2. Of these, 15 are non-split algebras and the nine remaining algebras are written as direct additions of n-Lie algebras of low-dimension and abelian n-Lie algebras. Originality/value – This classification of n-Lie algebras provides a complete understanding of these algebras that are used in algebraic studies.

Keywords

• Nilpotent n-lie algebra
• Classification
• Nilpotent n-Lie algebra of class 2