Polynilpotent capability of Lie algebras

Abstract

Let ${\mathcal{N}}_{c_1,\dots ,c_n}$ be the variety of polynilpotent Lie algebras of class row $(c_1,\dots ,c_n)$. In this article, we generalize the Ganea map and the notion of capability with respect to the variety ${\mathcal{N}}_{c_1,\dots ,c_n}$, and study their connections with the polynilpotent multipliers of Lie algebras. Furthermore, We determine the polynilpotent multipliers of some known Lie algebras and give the structure of all $(c_1,\dots ,c_n)$-capable nilpotent Lie algebras with derived subalgebra of dimension at most 1.

Keywords:

• Polynilpotent multiplier
• $(c_1,\dots ,c_n)$-capable
• nilpotent Lie algebra

2010 Mathematics Subject Classification:

• 17B05
• 17B30
• 17B99

Acknowledgements

The authors would like to thank the referee for his/her valuable suggestions, which have made the improvement of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.