Root system and representation of quivers / Sistema de raizes e representações de quivers

AUTOR(ES)

Vitor Moretto Fernandes da Silva

DATA DE PUBLICAÇÃO

2009

RESUMO

In this work, we define quivers and their representations, and discuss how the category of modules over an arbitrary connected associative algebra can be associated to the category of representations of a quiver. We also study the root system of the Cartan quadratic form associated to a quiver, which is bijective with the set of dimension vectors for which an indecomposable representation exists. The proof of Gabriel s Theorem, which characterizes all quivers with finitely many indecomposable representations in terms of its Cartan form, is presented. Gabriel s Theorem also defines when a quiver is of tame time. Finally, we also describe a theorem due to Ovsienko which, under certain conditions, characterize the quivers with relations that admit only finitely many indecomposable representations in terms of its Brenner form

ASSUNTO(S)

quivers representações de quivers sistema de raizes (algebra) root systems (algebra) representations of quivers quivers

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