“…It is shown in [1] (see also [8,Corollary 3.18]) that every Belavin-Drinfeld splitting of g ⊕ g is conjugate by an element in G diag to a splitting of the form (4.24) g ⊕ g = g diag + l ′′ S 2 ,T 2 ,d 2 ,V 2 , where (S 2 , T 2 , d 2 ) is a Belavin-Drinfeld triple in the sense that S d 2 2 = {α ∈ S 2 | d n 2 α is defined and is in S 2 for n = 1, 2, · · · } = ∅, and V 2 ∈ L space (z S 2 ⊕ z T 2 ) is such that h diag ∩ (V 2 + {(x, θ d 2 (x)) | x ∈ h S 2 } = 0. In other words, (4.24) is the special case of the splitting in (4.12) with l 1 = g diag .…”