New bounds on the dimension of the Schur multiplier of n-Lie algebras

Abstract

We give a bound on the dimension of the Schur multiplier of a finite-dimensional nilpotent n-Lie algebra, which sharpens the earlier bounds on the dimension of Schur multiplier of such n-Lie algebras. Then we give the structure of all nilpotent n-Lie algebras that attain this bound. Also, we obtain a new bound on the dimension of the Schur multiplier of a d-dimensional c-step nilpotent n-Lie algebra with the derived subalgebra of dimension d – n, which sharpens the earlier known bounds.

Keywords:

• Nilpotent n-Lie algebra
• Schur multiplier
• Capable n-Lie algebra
• maximal class

2020 Mathematics Subject Classification:

• 17B05
• 17B30
• 17B99

Acknowledgment

The authors would like to thank the referees for valuable suggestions.