Diameters of the Commuting Graphs of Simple Lie Algebras

摘要

Let L be a Lie algebra with center Z(L). The commuting graph Gamma(L) of L is a graph with vertex set L 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 F(g).