Stable autoequivalences of self-injective algebras of finite representation type

Abstract

In this work, a subgroup of the group of autoequivalences of the stable category for all standard self-injective algebras of finite representation type (which is referred to as the group of monomial autoequivalences) in computed, as well as the quotient group of this group modulo natural isomorphisms. If some restrictions on the type of the algebra are imposed, this subgroup coincides with the whole group of autoequivalences. Furthermore, these results are generalized to the case of mesh-categories associated with the quiver of the form $ {{{\mathbb{Z}T}} \left/ {G} \right.} $ , where T is an arbitrary tree and the group G is generated by the Auslander-Reiten translate. Bibliography: 4 titles.