5 problems

Let $A$ be a finitely generated PI-algebra over the field of rational numbers, and let $J$ be its Jacobson radical. Representability conjecture. If … then $A$ is representable. Thi…

Let $L$ be a finitely generated Lie PI-algebra. Write $\gamma_L(n)$ for its growth function, and let $\ln^{(q)}n$ denote the $q$-fold iterated natural logarithm. Intermediate-growt…

Let $F$ be an algebraically closed field of characteristic zero. Let $A$ be a finite-dimensional basic algebra with Wedderburn–Malcev decomposition … where $J(A)$ is the Jacobson r…

Let $W$ be an algebra over an algebraically closed field $F$ of characteristic zero satisfying a polynomial identity of degree $n$. Suppose that $W$ is nondegenerately graded by a…

Let $K$ be the ground field, let $E$ denote the Grassmann algebra, and let $R$ be a PI-algebra with … where each $R_i$ is one of $K$, $E$, $M_2(K)$, or $E\otimes_K E$, and at least…