4 problems

Racah algebra quotient conjecture. The centraliser for $sl_2$ is a quotient of $R(3)$.

Jacobi identity conjecture. In this remaining case, the Jacobi identity is satisfied without additional constraints.

Let $U(\mathfrak{sl}_2)$ act diagonally on the tensor product of any three irreducible representations, and let the centralizer be the algebra of endomorphisms commuting with this…

The higher rank Racah algebra is the algebraic structure associated with the intermediate Casimir elements in an $n$-fold tensor product of $\mathfrak{su}(1,1)$. Let…