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...
| Autores: | , , |
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| 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 |
| 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. |
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