THE FIRST HOCHSCHILD COHOMOLOGY GROUP OF A CLUSTER TILTED ALGEBRA REVISITED

Abstract

Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH 1(B) with coefficients in the B–B-bimodule B. If C is a tilted algebra such that B is the relation extension of C by [Formula: see text], then we prove that HH 1(B) is isomorphic, as a vector space, to the direct sum of HH 1(C) with HH 1(B,E). This yields homological interpretations for results of the first and the fourth authors with M. J. Redondo.