  We construct families of commutative (super) algebra objects in the category
of weight modules for the unrolled restricted quantum group
$\overline{U}_q^H(\mfg)$ of a simple Lie algebra $\mfg$ at roots of unity, and
study their categories of local modules. We determine their simple modules and
derive conditions for these categories being finite, non-degenerate, and
ribbon. Motivated by numerous examples in the $\mfg=\mathfrak{sl}_2$ case, we
expect some of these categories to compare nicely to categories of modules for
vertex operator algebras. We focus in particular on examples expected to
correspond to the higher rank triplet vertex algebra $W_Q(r)$ of Feigin and
Tipunin \cite{FT} and the $B_Q(r)$ algebras of \cite{C1}.
