The Commuting Graphs of Certain Solvable Lie Algebras
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909946479640576 |
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| author | Ha, Hieu V. Le, Vu A. Nguyen, Tuan A. Nguyen, Tuyen T. M. Quang, Hoa D. |
| author_facet | Ha, Hieu V. Le, Vu A. Nguyen, Tuan A. Nguyen, Tuyen T. M. Quang, Hoa D. |
| contents | Let $Z(\cal L)$ be the center of a Lie algebra $\cal L$ with Lie bracket $[\cdot, \cdot]$. %We then define The commuting graph of $\cal L$ is then defined by the simple undirected graph $Γ({\cal L})=(V_{\cal L},E_{\cal L})$ in which the vertex set is $V_{\mathcal L}=\mathcal L \setminus Z(\mathcal L)$ and the set of edges $E_{\cal L}=\left\{ \{x,y\} \mid [x,y] =0 \right\}$. The main purpose of this paper is to accurately describe the connected components of the commuting graph of solvable Lie algebras of dimension at most 4. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05755 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Commuting Graphs of Certain Solvable Lie Algebras Ha, Hieu V. Le, Vu A. Nguyen, Tuan A. Nguyen, Tuyen T. M. Quang, Hoa D. Rings and Algebras Let $Z(\cal L)$ be the center of a Lie algebra $\cal L$ with Lie bracket $[\cdot, \cdot]$. %We then define The commuting graph of $\cal L$ is then defined by the simple undirected graph $Γ({\cal L})=(V_{\cal L},E_{\cal L})$ in which the vertex set is $V_{\mathcal L}=\mathcal L \setminus Z(\mathcal L)$ and the set of edges $E_{\cal L}=\left\{ \{x,y\} \mid [x,y] =0 \right\}$. The main purpose of this paper is to accurately describe the connected components of the commuting graph of solvable Lie algebras of dimension at most 4. |
| title | The Commuting Graphs of Certain Solvable Lie Algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2512.05755 |