• Corpus ID: 236087426

# 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}
}
• Published 17 July 2021
• Mathematics
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
The centroid of extended affine and root graded Lie algebras
• Mathematics
• 2005
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,
On Lie-isoclinic Leibniz algebras
• Mathematics
• 2016
INVARIANT BILINEAR FORMS ON LIE SUPERALGEBRAS
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
An algorithm for the classification of 3-dimensional complex Leibniz algebras
• Mathematics
• 2012
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,
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9288991093635559, "perplexity": 2280.36863259522}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103943339.53/warc/CC-MAIN-20220701155803-20220701185803-00568.warc.gz"}