caa a22 4500 60616071X CHVBK 20210128100631.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10468-015-9551-x doi (NATIONALLICENCE)springer-10.1007/s10468-015-9551-x On the First Hochschild Cohomology Group of a Cluster-Tilted Algebra [Elektronische Daten] [Ibrahim Assem, María Redondo, Ralf Schiffler] 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, then we show that if B is tame, then HH1(B) is isomorphic, as a k-vector space, to the direct sum of HH 1 ( C ) ${\text {HH}}^{1}(C)$ with k n B , C $k^{n_{B,C}}$ , where n B,C is an invariant linking the bound quivers of B and C. In the representation-finite case, HH1(B) can be read off simply by looking at the quiver of B. Springer Science+Business Media Dordrecht, 2015 Cluster-tilted algebra nationallicence Hochschild cohomology nationallicence Assem Ibrahim Département de Mathématiques, Université de Sherbrooke, J1K 2R1, Sherbrooke, Québec, Canada aut Redondo María Departamento de Matemática, Universidad Nacional del Sur, Av. Alem 1253, 8000, Bahía Blanca, Argentina aut Schiffler Ralf Department of Mathematics, University of Connecticut, 06268, Storrs, CT, USA aut Algebras and Representation Theory Springer Netherlands 18/6(2015-12-01), 1547-1576 1386-923X 18:6<1547 2015 18 10468 https://doi.org/10.1007/s10468-015-9551-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-015-9551-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Assem Ibrahim Département de Mathématiques, Université de Sherbrooke, J1K 2R1, Sherbrooke, Québec, Canada aut NATIONALLICENCE 700 1- Redondo María Departamento de Matemática, Universidad Nacional del Sur, Av. Alem 1253, 8000, Bahía Blanca, Argentina aut NATIONALLICENCE 700 1- Schiffler Ralf Department of Mathematics, University of Connecticut, 06268, Storrs, CT, USA aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/6(2015-12-01), 1547-1576 1386-923X 18:6<1547 2015 18 10468