13 problems

Let $K=\Bbbk G$ for a finite group $G$, and let … be a finite-dimensional coradically graded connected Hopf algebra, with $R^1$ its degree-one component. Andruskiewitsch–Schneider…

A pointed Hopf algebra is a Hopf algebra whose coradical is a group algebra. The class under consideration consists of Hopf algebras generated by skew-primitive elements and an abe…

Let $A$ be a finite-dimensional pointed Hopf algebra, and let $p$ be a prime divisor of $\dim A$. A group-like element of order $p$ is an element $g$ with $\Delta(g)=g\otimes g$ an…

Let $A$ be a finite-dimensional pointed Hopf algebra over an algebraically closed field of characteristic $0$. Its group-like elements are elements $g$ satisfying…

Let $A$ be a finite-dimensional pointed Hopf algebra over an algebraically closed field of characteristic zero. Its group-like elements and skew-primitive elements are the elements…

Let $G$ be a finite simple non-abelian group, and let $D(G)$ be its Drinfeld double. A finite-dimensional Nichols algebra associated with a $D(G)$-module is a Nichols algebra arisi…

Kochetov's conjecture. The smash product $H\#\mathbb{F}G$ is PI if and only if

Folklore conjecture. Then $H$ is the group algebra $\mathbb{C}G(H)$.

Let $L$ be a cosemisimple Hopf algebra and let $A$ be a pointed Hopf algebra with diagram $\mathcal R$ and infinitesimal braiding $\mathcal V=\mathcal R^1$ in…

Let $H$ be a pointed Hopf algebra. Say that $H$ has rank one when $C_1(H)$ is a free left $C_0(H)$-module of rank two, and let $\operatorname{PCdim} H$ denote its primitive cohomol…

Let $\Bbbk$ be an algebraically closed field of characteristic zero, and let $H$ be a finite-dimensional pointed Hopf algebra over $\Bbbk$. An element $g\in H$ is grouplike if…

Assume that $k$ is an algebraically closed field of characteristic zero. A Hopf algebra is pointed when its coradical is spanned by grouplike elements; its grouplike and skew primi…

Generation conjecture. Every finite-dimensional pointed Hopf algebra is generated as an algebra by grouplike and skew-primitive elements.