On the First Hochschild Cohomology Group of a Cluster-Tilted Algebra

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 kvector space, to the direct sum of HH...

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Detalhes bibliográficos
Autores: Assem, Ibrahim, Redondo, Maria Julia, Schiffler, Ralf
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2015
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositório:CONICET Digital (CONICET)
Idioma:inglês
OAI Identifier:oai:ri.conicet.gov.ar:11336/11872
Acesso em linha:http://hdl.handle.net/11336/11872
Access Level:Acceso aberto
Palavra-chave:Cluster-Tilded Algebra
Hochschild Cohomology
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descrição
Resumo: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 kvector space, to the direct sum of HH1(C) with knB,C , where nB,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.