On translation quivers with weak sections

Alvares, Edson Ribeiro; Coelho, Flávio U.

doi:10.1090/fic/045/01

Representations of Algebras and Related Topics 2005

DOI: 10.1090/fic/045/01

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On translation quivers with weak sections

Edson Ribeiro Alvares¹,

Flávio U. Coelho²

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“…Finally, in Section 5, we state and prove our main result. In [2], we look, in a different direction, at another generalization of Li's result. This problem has also been considered in a different way in [1].…”

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Embeddings of Non-semiregular Translation Quivers in Quivers of Type $\mathbb{Z}\Delta$

Alvares

Coelho

2006

Algebr Represent Theor

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In this work we show that a directed translation quiver such that every path from a injective vertex to a projective vertex that has at most two hooks and in case two, they are consecutives, can be embedded in a quiver Z . This generalizes a result by (Li, Comm. Algebra, 28(10),4635-4645, 2000). Mathematics Subject Classifications (2000) 16G70 · 16G20 · 16E10The Auslander-Reiten quiver (AR-quiver, for short) A of a given Artin algebra A plays an important role in the understanding of the category of A-modules. One way to study the shape of a component is through its embedding in another component which is easier to describe, see for instance [10] where this idea has been successfully used. In [9], S. Li has considered the problem of embeddings of a component of A without oriented cycles into translation quivers of type Z , where is a section of . His main result states that such an embedding exists if and only if any path in from an injective to a projective is sectional (see Section 1 for definitions).

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confidence: 99%

Embeddings of Non-semiregular Translation Quivers in Quivers of Type $\mathbb{Z}\Delta$

Alvares

Coelho

2006

Algebr Represent Theor

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Organising the module category

Coelho

2021

São Paulo J. Math. Sci.

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On translation quivers with weak sections

Cited by 2 publications

References 0 publications

Embeddings of Non-semiregular Translation Quivers in Quivers of Type $\mathbb{Z}\Delta$

Embeddings of Non-semiregular Translation Quivers in Quivers of Type $\mathbb{Z}\Delta$

Organising the module category

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