Stable autoequivalences of selfinjective algebras of finite representation type

In this work we compute the subgroup of the group of autoequivalences of stable category for all standard selfinjective algebras of finite representation type (which we call the group of monomial autoequivalences), also we compute the quotient group of this group modulo natural isomorphisms. If we impose some restrictions on the type of the algebra this subgroup coincides with the whole group of autoequivalences. Furthermore, we generalize these results to the case of mesh-categories associated to the quiver of the form $\mathbb ZT/G,$ where $T$ is an arbitrary tree and the group $G$ is generated by Auslander–Reiten translate.