English

Diameter of Commuting Graphs of Lie Algebras

Rings and Algebras 2024-05-13 v1

Abstract

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 44.

Keywords

Cite

@article{arxiv.2405.06521,
  title  = {Diameter of Commuting Graphs of Lie Algebras},
  author = {Hieu V. Ha and Hoa D. Quang and Vu A. Le and Tuyen T. M Nguyen},
  journal= {arXiv preprint arXiv:2405.06521},
  year   = {2024}
}

Comments

21 pages