5 problems

Let $L$ be a simple complex Lie algebra. A grading of $L$ is called fine if it cannot be properly refined by another grading, and a fine group grading is a fine grading whose index…

Let $L$ be a Lie algebra with a group grading $\Gamma$ that is a coarsening of an abelian grading of $L$. Abelianness conjecture. Then $\Gamma$ is abelian. The paper states that no…

Classification conjecture. The algebra $A$ is $*$-graded simple if and only if it is isomorphic as a graded $*$-algebra either to the $G$-graded simple algebra…

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…

Bahturin–Zaicev conjecture. One has