All Questions

Let $\mathfrak{g}$ be a semisimple Lie algebra. Let $U_h(\mathfrak{g})$ be the Drinfeld-Jimbo quantum group, i.e. the $\mathbb{C}[[h]]$-algebra topologically generated by $X_i,Y_i,H_i$ where $1\leq i\...

I am interested in the braided dual of the quantum group $U_q(\frak{sl_2})$. This is the algebra generated by the matrix coefficients but where the multiplication is twisted by an action of the $R$-...

Question Let $H$ be a finite dimensional complex Hopf algebra and $D(H)$ its quantum double. Can we classify the simple objects in $\operatorname{Rep}D(H)$ if the representations of $H$ are well-...

I am using this definition: An algebra of functions on a finite quantum group $\mathbb{G}$ is a finite dimensional $C^\ast$-Hopf algebra $A=:F(\mathbb{G})$. I have the following (very well known --...

I've come across a reference in a paper to the Hecke relation for the universal R-matrix of a quasi-triangular Hopf algebra. I've looked around, standard references, online etc, but can't seem to ...

2-cocycle twists of Hopf algebras Let $H$ be a Hopf algebra over a field $k$. Then a (left, unital) 2-cocycle on $H$ is a map $$ f: H \otimes H \to k$$ such that $$ f(x_{(1)},y_{(1)})f(x_{(2)} y_{(...