Yang-Baxter equations on matrix dialgebras with a bar unit (Q2484476)

In the paper by using the relationship between Leibniz algebras and dialgebras, the Yang-Baxter equation for dialgebra \[ [T^{23},T^{13}]+[T^{23},T^{12}]-[T^{12},T^{13}]=0 \] is derived (Eq. (6) in the paper). Unfortunately, this equation is not true in general which should be \[ [T^{23},T^{13}]+[T^{23},T^{12}]\vdash E-[T^{12},T^{13}]=0. \]