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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

The Path Algebra as a Left Adjoint Functor

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Author(s):
Iusenko, Kostiantyn [1] ; MacQuarrie, John William [2]
Total Authors: 2
Affiliation:
[1] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil
[2] Univ Fed Minas Gerais, Belo Horizonte, MG - Brazil
Total Affiliations: 2
Document type: Journal article
Source: ALGEBRAS AND REPRESENTATION THEORY; v. 23, n. 1, p. 33-52, FEB 2020.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 14/09310-5 - Algebraic structures and their representations
Grantee:Vyacheslav Futorny
Support Opportunities: Research Projects - Thematic Grants