The Path Algebra as a Left Adjoint Functor

Autor(es)

Iusenko, Kostiantyn ^[1] ; MacQuarrie, John William ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil

^[2] Univ Fed Minas Gerais, Belo Horizonte, MG - Brazil

• Tipo de documento: Artigo Científico
• Fonte: ALGEBRAS AND REPRESENTATION THEORY; v. 23, n. 1, p. 33-52, FEB 2020.
• Citações Web of Science: 0

Resumo

We consider an intermediate category between the category of finite quivers and a certain category of pseudocompact associative algebras whose objects include all pointed finite dimensional algebras. We define the completed path algebra and the Gabriel quiver as functors. We give an explicit quotient of the category of algebras on which these functors form an adjoint pair. We show that these functors respect ideals, obtaining in this way an equivalence between related categories. (AU)

• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático