4 problems

Let … be a semisimple finite-dimensional associative algebra over a field $F$ of characteristic zero. Conjecture 2. Then [the source statement is truncated before giving the assert…

Let $t_n(F)$ denote the subalgebra of non-strictly upper-triangular matrices in $M_n(F)$, and let $\operatorname{rb}_0(t_n(F))$ denote its zero-weight Rota–Baxter index. Conjecture…

Let $\Bbbk[x]$ be the polynomial algebra in one variable, and let … be the collection of injective Rota–Baxter operators of weight zero described in the source. Classification conj…

Let $A$ be a semisimple finite-dimensional associative algebra over a field $F$ of characteristic zero, decomposed as … where each $A_i$ is simple. Write $\operatorname{rb}(A)$ for…