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arXiv · 1209.2146

The first Hochschild cohomology group of a cluster-tilted algebra revisited

Ibrahim Assem·Juan Carlos Bustamante·Kiyoshi Igusa·Ralf Schiffler
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Abstract

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.

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Ibrahim Assem, Juan Carlos Bustamante, Kiyoshi Igusa, Ralf Schiffler. 2013-03-12. The first Hochschild cohomology group of a cluster-tilted algebra revisited. https://arxiv.org/abs/1209.2146

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