Rational solutions of the classical Yang-Baxter equation and quasi Frobenius Lie algebras Original Research Article

In this paper we establish a relation between rational solutions of the classical Yang-Baxter equation for sℓ(n) of class k and subalgebras of sℓ(n + k) having a 2-cocycle, which is nondegenerate as a bilinear form. This is a generalization of the result about rational solutions obtained by Belavin and Drinfeld [A. Belavin, V. Drinfeld, On classical Yang-Baxter equation for simple Lie algebras, Funct. Anal. Appl. 16 (1982) 1–29], which is exactly the case k = 0.