Let A be a complex diagonalizable matrix with two distinct nonzero eigenvalues λ and μ, the Yang-Baxter-like matrix equation AXA = XAX is reconsidered. We correct and improve the results in Shen et al ...

The main purpose of this note is to prove that any basis of a nilpotent Lie algebra for which all diagonal left-invariant metrics have diagonal Ricci tensor necessarily produce quite a simple set of ...