\def\g{{\frak g}} Let $L$ be a Lie algebra with center $Z(L)$. The commuting graph $\Gamma(L)$ of $L$ is a graph with vertex set $L\setminus Z(L)$, two distinct vertices $x$ and $y$ are adjacent if and only if $x$ and $y$ commute, i.e., $[x,y]=0$. Let $\g$ be a finite-dimensional simple Lie algebra over an algebraically closed field of characteristic zero. In this paper, we study the diameter of $\Gamma(\g)$.
1
Dept. of Mathematics, University of Mining and Technology, Xuzhou 221116, P. R. China
Dengyin Wang; Chunguang Xia. Diameters of the Commuting Graphs of Simple Lie Algebras. Journal of Lie Theory, Tome 27 (2017) no. 1, pp. 139-154. http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a6/
@article{JOLT_2017_27_1_a6,
author = {Dengyin Wang and Chunguang Xia},
title = {Diameters of the {Commuting} {Graphs} of {Simple} {Lie} {Algebras}},
journal = {Journal of Lie Theory},
pages = {139--154},
year = {2017},
volume = {27},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a6/}
}
TY - JOUR
AU - Dengyin Wang
AU - Chunguang Xia
TI - Diameters of the Commuting Graphs of Simple Lie Algebras
JO - Journal of Lie Theory
PY - 2017
SP - 139
EP - 154
VL - 27
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a6/
ID - JOLT_2017_27_1_a6
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%U http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a6/
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