Finding a cluster-tilting object for a representation finite cluster-tilted algebra
We provide a technique to find a cluster-tilting object having a given cluster-tilted algebra as endomorphism ring in the finite type case.
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 R be a split extension of an artin algebra A by a nilpotent bimodule , and let M be an indecomposable non-projective A-module. We show that the almost split sequences ending with M in mod A and mod R coincide if and only if = 0 and .