3-Dimensional Skew-symmetric Algebras and the Variety of Hom-Lie Algebras-Reference-Cited by-同舟云学术

3-Dimensional Skew-symmetric Algebras and the Variety of Hom-Lie Algebras

Published:2018-12 Issue:04 Volume:25 Page:547-566
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Remm Elisabeth¹

Affiliation:

1. LMIA, Université de Haute-Alsace (LMIA, EA 3993), F-68100 Mulhouse, France

Abstract

An algebra is called skew-symmetric if its multiplication operation is a skewsymmetric bilinear application. We determine all these algebras in dimension 3 over a field of characteristic different from 2. As an application, we determine the subvariety of 3-dimensional Hom-Lie algebras. For this type of algebra, we study also the case of dimension 4.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S100538671800038X

Reference8 articles.

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2. A Class of Nonassociative Algebras

3. Deformations of Lie algebras using σ-derivations

4. Lie type algebras with an automorphism of finite order

5. Algebras with one operation including Poisson and other Lie-admissible algebras

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1. On 4-dimensional Hom-Lie Algebras;Springer Proceedings in Mathematics & Statistics;2024

2. Hom-Lie Superalgebras in Characteristic 2;Mathematics;2023-12-14

3. On the classification of 3-dimensional complex hom-Lie algebras;Journal of Pure and Applied Algebra;2023-05

4. $\mathbb{Z}$-graded Hom-Lie superalgebras;Publicationes Mathematicae Debrecen;2022-10-01

5. A commutative algebra approach to multiplicative Hom-Lie algebras;Linear and Multilinear Algebra;2022-03-17