Some properties of Camina and $n$-Baer Lie algebras
Let $I$ be a non-zero proper ideal of a Lie algebra $L$. Then $(L, I)$ is called a Camina pair if $I \subseteq [x,L]$, for all $x \in L\setminus I$. Also, $L$ is called a Camina Lie algebra if $(L, L^2)$ is a Camina pair. We first give some properties of Camina Lie algebras, and then show that all C...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Shahid Bahonar University of Kerman
2024-12-01
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| Series: | Journal of Mahani Mathematical Research |
| Subjects: | |
| Online Access: | https://jmmrc.uk.ac.ir/article_4485_ee2c6e4417c7cc259648988ae7b65809.pdf |
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| Summary: | Let $I$ be a non-zero proper ideal of a Lie algebra $L$. Then $(L, I)$ is called a Camina pair if $I \subseteq [x,L]$, for all $x \in L\setminus I$. Also, $L$ is called a Camina Lie algebra if $(L, L^2)$ is a Camina pair. We first give some properties of Camina Lie algebras, and then show that all Camina Lie algebras are soluble. Also, a new notion of $n$-Baer Lie algebras is introduced, and we investigate some of its properties, for $n=1, 2$. A Lie algebra $L$ is said to be $2$-Baer if for any one dimensional subalgebra $K$ of $L$, there exists an ideal $I$ of $L$ such that $K$ is an ideal of $I$. Finally, we study three classes of Lie algebras with $2$-subideal subalgebras and give some relations among them. |
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| ISSN: | 2251-7952 2645-4505 |