We provide a technique to find a cluster-tilting object having a given cluster-tilted algebra as endomorphism ring in the finite type case.

Let K be a field of characteristic p > 0, K* the multiplicative group of K and $G=G_p\times B$ a finite group, where $G_p$ is a p-group and B is a p’-group. Denote by $K^{\lambda }G$ a twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for G to be of OTP projective K-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,K*) such that every indecomposable $K^{\lambda }G$-module is isomorphic to the outer tensor product V W of an indecomposable $K^{\lambda }{G}_p$-module V and a simple...

Let S be a commutative complete discrete valuation domain of positive characteristic p, S* the unit group of S, Ω a subgroup of S* and $G=G_p\times B$ a finite group, where $G_p$ is a p-group and B is a p’-group. Denote by $S^{\lambda }G$ the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). For Ω satisfying a specific condition, we give necessary and sufficient conditions for G to be of OTP projective (S,Ω)-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,Ω) such that every indecomposable...

We show that the mutation class of a coloured quiver arising from an m-cluster tilting object associated with a finite-dimensional hereditary algebra H, is finite if and only if H is of finite or tame representation type, or it has at most two simples. This generalizes a result known for cluster categories.

Let G be a finite group, K a field of characteristic p > 0, and $K^{\lambda }G$ the twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for $K^{\lambda }G$ to be of semi-wild representation type in the sense of Drozd. We also introduce the concept of projective K-representation type for a finite group (tame, semi-wild, purely semi-wild) and we exhibit finite groups of each type.