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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.06521 |
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| _version_ | 1866911873017839616 |
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| author | Ha, Hieu V. Quang, Hoa D. Le, Vu A. Nguyen, Tuyen T. M |
| author_facet | Ha, Hieu V. Quang, Hoa D. Le, Vu A. Nguyen, Tuyen T. M |
| contents | In this paper, we study the connectedness of the commuting graph of a general Lie algebra and provide a process to determine whether the commuting graph is connected or not, as well as to compute an upper bound for its diameter. In addition, we will examine the connectedness and diameter of the commuting graphs of some remarkable classes of Lie algebras, including: (1) a class of Lie algebras with one- or two-dimensional derived algebras; and (2) a class of solvable Lie algebras over the real field of dimension up to $4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06521 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diameter of Commuting Graphs of Lie Algebras Ha, Hieu V. Quang, Hoa D. Le, Vu A. Nguyen, Tuyen T. M Rings and Algebras 17B30, 17B60 In this paper, we study the connectedness of the commuting graph of a general Lie algebra and provide a process to determine whether the commuting graph is connected or not, as well as to compute an upper bound for its diameter. In addition, we will examine the connectedness and diameter of the commuting graphs of some remarkable classes of Lie algebras, including: (1) a class of Lie algebras with one- or two-dimensional derived algebras; and (2) a class of solvable Lie algebras over the real field of dimension up to $4$. |
| title | Diameter of Commuting Graphs of Lie Algebras |
| topic | Rings and Algebras 17B30, 17B60 |
| url | https://arxiv.org/abs/2405.06521 |