8 problems

Let ${\mathcal M}$ be the space of quasi-triangular solutions to the classical Yang–Baxter equation, and let $r_{CG}(i,n)$ be the Cremmer–Gervais $r$-matrix indexed by positive cop…

Let $m$ and $n$ be relatively prime positive integers with $m<n$. Let $\mathfrak{p}_{m,n}\subseteq\mathfrak{sl}_n$ be the maximal parabolic subalgebra obtained by deleting the $m$-…

Let $N$ be the matrix size, let $z,w,z_1,z_2,z_3$ be spectral parameters, and let ${\bf r}_{12}(z,w)$ be the limiting skew-symmetric matrix defined by the formulas in the preceding…

Let $\frak p_i$ be the maximal parabolic subalgebra of $\frak{sl}(n)$ obtained by deleting the negative simple root $e_{i+1,i}$. Suppose that $i$ and $n$ are relatively prime. The…

Necessity conjecture. All solutions of the classical Yang–Baxter equation are described by the preceding ansatz and differential-equation condition. The statement is presented as t…

Let $n$ be a positive integer, let ${\mathfrak g}$ be a Lie algebra, and let $r\in {\mathfrak g}\otimes {\mathfrak g}$ solve the classical Yang–Baxter equation (CYBE). Let…

Let $A$ be a unital Jordan algebra, and consider trigonometric and quasi-trigonometric solutions of the $A$-classical Yang–Baxter equation (A-CYBE). Jordan unitality obstruction co…

Let $A$ be a unital non-associative strongly geometrically admissible algebra, and consider solutions of the $A$-classical Yang–Baxter equation (A-CYBE) of trigonometric or quasi-t…