Um estudo sobre álgebras associadas a alguns grafos orientados em níveis

• Autor(a) principal: Dirino, Kariny de Andrade
• Data de Publicação: 2017
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/7784
• topic: Grafos orientados em níveis; Álgebras associadas a grafos; Série de Hilbert; Grupo de automorfismos; Grafo de Petersen; Koszulidade; Layered directed graphs; Algebras associated to graphs; Hilbert series; Automorphism group; Petersen graph; Koszuality; MATEMATICA::ALGEBRA

Considering a layered directed graphs we may associate it to an algebra, denoted as , whose generators are the edges of the graph and the relations are defined through: every ways with the same initial vertex and the same final vertex determine different fractorizations for the same polynomial with coefficients in a non-commutative ring. We present a study about these algebras and their main properties, presenting some classes of examples and having as central focus the Hasse graph of the partially ordered set of k -faces of Petersen graph, . We discuss the results on basis for algebras of type we calculate their Hilbert series and the automorphisms group of these algebras, we determine the subgraphs induced by the set of vertices fixed by each and we calculate the graded trace generating functions, in order to introduce problems related to koszulity.