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Some quantities associated to finite dimensional Hopf algebras

let $(H,\Delta,m,s)$ be a Hopf algebra. To this Hopf algebra one can associate two obvious linear maps $T_H, S_H: H \to H $ with $T_H=m\circ \Delta,\quad S_H=s$. Are there two finite dimensional ...
Ali Taghavi's user avatar
26 votes
1 answer
2k views

Have the Quantum Group Theorists taught the Group Theorists Anything?

I will start with the general before moving to the specific. Consider for a moment the two (very) soft definitions. An abstraction of an object $X$ is a category $\mathcal{C}_0$ such that $X$ ...
JP McCarthy's user avatar
  • 1,037
4 votes
0 answers
67 views

Is the associated grouplike $\gamma=uS(u)^{-1}$ of a quasi-triangular Hopf algebra always the square of another grouplike?

Let $(H,R)$ be a finite-dimensional quasi-triangular Hopf algebra, lets say generated by group-like and skew-primitive elements (I actually need it for $H$ fin. dim. pointed with $G(H)$ abelian). Let $...
Bipolar Minds's user avatar