On some properties of $\mathsf{Lie}$-centroids of Leibniz algebras
@inproceedings{Casas2021OnSP, title={On some properties of \$\mathsf\{Lie\}\$-centroids of Leibniz algebras}, author={Jos{\'e} Manuel Casas and Xabier Garc'ia-Mart'inez and Natalia Pachego-Rego}, year={2021} }
We study some properties on Lie-centroids related to central Liederivations, generalized Lie-derivations and almost inner Lie-derivations. We also determine the Lie-centroid of the tensor product of a commutative associative algebra and a Leibniz algebra.
References
SHOWING 1-10 OF 43 REFERENCES
Algebraic exponentiation for Lie algebras.
- Mathematics
- 2020
It is known that the category of Lie algebras over a ring admits algebraic exponents. The aim of this paper is to show that the same is true for the category of internal Lie algebras in an additive,…
INVARIANT BILINEAR FORMS ON LIE SUPERALGEBRAS
- Mathematics
- 2004
This paper investigates Lie supseralgebras by definning the centroid and the zero degree centroid on them. The authors prove that for a quadratic Lie superalgebra (G,B), there is a 1-1 correspondence…
THE TENSOR CATEGORY OF LINEAR MAPS AND LEIBNIZ ALGEBRAS
- Mathematics
- 1998
AbstractWe equip the category
$$\mathcal{L}\mathcal{M}$$
of linear maps of vector spaces with a tensor product which makes it suitable for various constructions related to Leibniz algebras. In…
The Schur Lie-multiplier of Leibniz algebras
- Mathematics
- 2017
Abstract For a free presentation 0 → τ → → → 0 of a Leibniz algebra , the Baer invariant is called the Schur multiplier of relative to the Liezation functor or Schur Lie-multiplier. For a two-sided…
Lie-central derivations, Lie-centroids and Lie-stem Leibniz algebras
- Mathematics
- 2019
In this paper, we introduce the notion Lie-derivation. This concept generalizes derivations for non-Lie Leibniz algebras. We study these Lie-derivations in the case where their image is contained in…
Lie-isoclinism of pairs of Leibniz algebras
- Mathematics
- 2018
The aim of this paper is to consider the relation between Lie-isoclinism and isomorphism of two pairs of Leibniz algebras. We show that, unlike the absolute case for finite dimensional Lie algebras,…