Subprime solutions of the classical Yang-Baxter equation (Q1989808)

It is well known that Yang-Baxter equations are crucial in the study of mathematics and physics. In this paper, the author introduces a new family of classical \(r\)-matrices for the Lie algebra \(sl_n\) that lies in the Zariski boundary of the Belavin-Drinfeld space \(M\) of quasi-triangular solutions to the classical Yang-Baxter equation, and proves the conjecture in the cases when \(n\equiv \pm 1 \pmod i\): Gerstenhaber and Giaquinto stated that the boundaries of the Cremmer-Gervais components contained \(r\)-matrices having maximal parabolic subalgebras \(p_{i,n}\subseteq sl_n\) as carriers, and conclude with a proof of the Gerstenhaber-Giaquinto boundary conjecture in a case unrelated to the subprime cases.