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

Ibrahim Assem (1) , Maria Julia Redondo (2) , Ralf Schiffler (3)

1 UdeS - Département de mathématiques [Sherbrooke]
2 UNS - Universidad Nacional del Sur [Argentina]
3 UCONN - University of Connecticut

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.

Mots clés: Hochschild cohomology; cluster-tilted algebra

Domaines: Théorie des représentations [math.RT]

Ibrahim Assem, Maria Julia Redondo, Ralf Schiffler. On the first Hochschild cohomology group of a cluster-tilted algebra. 2012. ⟨hal-00686049v2⟩