The first Hochschild cohomology group of a cluster-tilted algebra   revisited
  Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH1(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 E= Ext2(DC,C), then we prove that HH1(B) is isomorphic, as a vector space, to the direct sum of HH1(C) with HH1(B,E). This yields homological interpretations for results of the first and the fourth author with M.J. Redondo. 
Ibrahim Assem, Juan Carlos Bustamante, Kiyoshi Igusa and Ralf   Schiffler
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