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A very well-known theorem in Hopf algebra theory (see, for example, Lorenz - A tour of representation theory or the EGNO book (Etingof, Gelaki, Nikshych, and Ostrik - Tensor categories)) states that ...

Throughout let $p$ be a prime, and let $k$ be a field of characteristic $p$. Let $G$ be a compact Lie group. Such a $G$ can always be embedded as a closed subgroup of $SU(n)$ for some $n$. This ...