Stable representations of posets

Autor(es)

Futorny, Vyacheslav ^[1] ; Iusenko, Kostiantyn ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Pure and Applied Algebra; v. 223, n. 12, p. 5251-5278, DEC 2019.
• Citações Web of Science: 0

Resumo

The purpose of this paper is to study stable representations of partially ordered sets (posets) and compare it to the well known theory for quivers. In particular, we prove that every indecomposable representation of a poset of finite type is stable with respect to some weight and construct that weight explicitly in terms of the dimension vector. We show that if a poset is primitive then Coxeter transformations preserve stable representations. When the base field is the field of complex numbers we establish the connection between the polystable representations and the unitary chi-representations of posets. This connection explains the similarity of the results obtained in the series of papers. (C) 2019 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 15/00116-4 - Representações estáveis de posets e suas aplicações
• Beneficiário: Kostiantyn Iusenko
• Modalidade de apoio: Auxílio à Pesquisa - Regular