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arXiv · 1204.1607

On the first Hochschild cohomology group of a cluster-tilted algebra

Ibrahim Assem·Maria Redondo·Ralf Schiffler
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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, then we show that if C is constrained, or else if B is tame, then HH^1(B) is isomorphic, as a k-vector space, to the direct sum of HH^1(C) with k^{n\_{B,C}}, where n\_{B,C} is an invariant linking the bound quivers of B and C. In the representation-finite case, HH^1(B) can be read off simply by looking at the quiver of B.

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Ibrahim Assem, Maria Redondo, Ralf Schiffler. 2012-04-07. On the first Hochschild cohomology group of a cluster-tilted algebra. https://arxiv.org/abs/1204.1607

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