Representações torcidas de Quivers / Twisted representations of quivers

AUTOR(ES)

Daniela Moura Prata

DATA DE PUBLICAÇÃO

2008

RESUMO

The main goal of this thesis is to introduce for the category of twisted representations of a quiver Q the definitions and results one already knows for categories of representations of quivers. The concept of twisted representations was introduced by Gothen and King in [11] to study problems concerning vector bundles over algebraic varieties. King also showed in [16] that under certain conditions, semi-stable representations of a quiver are parametrized by an irreducible, normal projective algebraic variety. We show that we have the same results for twisted representations. Our main and original result provides an equivalence between the category of twisted representations of a quiver Q, RepMQ, and the category of representations of a quiver Q, Rep ˜Q, where ˜Q depends on Q and on the twisting factors. With this equivalence we developed the existing theory of representations of quivers for twisted representations, we rewrote classical results like Gabriel’s theorem and Kac’s theorem for the category of twisted representations and found a relation between RepQ and RepMQ.

ASSUNTO(S)

representations of quivers quivers categorias (matematica) quivers categories (mathematics) representações de quivers

Documentos Relacionados

• Geometric invariant theory and representations of quivers
• Representations of quivers and vector bundles over projectives spaces = : Representações de quivers e fibrados vetoriais sobre espaços projetivos
• Root system and representation of quivers
• Área e discretude de representações
• Representações retangulares de grafos planares