Sobre uma classe de álgebras associadas a duas famílias de grafos orientados

• Autor(a) principal: Barboza, Marcelo Bezerra
• Data de Publicação: 2015
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/4541
• topic: Grafos orientados em níveis; Álgebras associativas livres; Série de Hilbert; Grupo de automorfismos; Directed layered graphs; Free associative algebras; Hilbert series; Automorphism group; CIENCIAS EXATAS E DA TERRA::MATEMATICA

Given a directed layered graph , we present the algebra A() as a quotient of the free associative or tensor algebra (with unit, over an arbitrarily fixed field of scalars), freely generated by the set of edges in . We calculate the Hilbert series associated with the grading on A() coming from degree in the tensor algebra. We also calculate the group of automorphisms of A() that preserve the (ascending) filtration associated with the grading mentioned above. Despite the fact the main results within this notes remain true for a relatively large class of directed graphs, we stay close to the ones Dn and Ln, n 3, that is, those consisting, respectively, on the Hasse diagram of the partially ordered sets of faces in a regular polygon containing n edges and the power set of {1, . . . , n}. The work teaching us all of the above is [1], by Colleen Duffy.