Regarding $\mathrm{SL}(2)$ and $\mathfrak{sl}(2)$, may I know what is the difference between them?
I understand that $\mathrm{SL}(2)$ is the set of $2\times 2$ matrices with determinant $1$.
$\mathfrak{sl}(2)$ is refered in the book (Quantum Groups by Kassel) as a Lie algebra.
Sincere thanks for this beginner question.