On the dimension of the c-nilpotent Schur Lie-multiplier of Leibniz algebras

Abstract

The Schur $Lie$-multiplier of Leibniz algebras is the Schur multiplier of Leibniz algebras defined relative to the Liezation functor. In this paper, we provide upperbounds for the dimensions of the c-nilpotent Schur $Lie$-multiplier and c-$Lie$ stem cover of a finite-dimensional non-Lie Leibniz algebra. In the case of a $Lie$-nilpotent non-Lie Leibniz algebra, we determine this upperbound in terms of the dimensions of its $Lie$-center and $Lie$-commutator. We also investigate the case of c-nilpotent Leibniz algebras of maximal class.

Keywords:

• c-Lie-central extension
• c-$Lie$-stem cover
• c-nilpotent Schur $Lie$-multiplier

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 17A32
• 17B30
• 17B55

View correction statement:

Correction to: On the Dimension of the c-Nilpotent Schur Lie-Multiplier of Leibniz Algebras

Acknowledgements

We are indebted to the referee for very useful comments and remarks.