2015-04-222014-11-20VASCONCELOS, J. E. S. Álgebras associadas a grafos orientados em níveis e a propriedade da Koszulidade. 2014. 166 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2014.http://repositorio.bc.ufg.br/tede/handle/tede/4444In this work we study classes of algebras associated with layered directed graphs. Let be a layered directed graph. We determine the algebra Apq; generated by the edges of the graph, satisfying a set of quadratic relations R; and the dual algebra Apq!, associated with grpApqq. For each P Autpq we determine: the algebra Ap q; where is the subgraph of whose vertices are xed by ; the graded trace generating functions Tr pApq; tq and Tr pApq!; tq: We also determine the multiplicities of the irreducible representations of AutpApqq acting on Apq and Apq!: We show that for a layered directed graph , satisfying some hypotheses, AutpApqq K Autpq. Finally, we verify the property Tr pApq; tq Tr pApq!; tq 1 for all P Autpq, called koszulity property. We consider two classes of algebras, the algebra associated to the Hasse graph of the partially ordered set of faces of a star polygon, Ap q; and the algebra associated with the Hasse graph of the lattice of subespaces of a nite dimensional vector space over Fq; ApLpn; qqq:application/pdfAcesso AbertoGrafos orientados em níveisFunções geradoras do traço graduadoRepresenta ções irredutíveisMultiplicidadesPropriedade da koszulidadeLayered directed graphsGraded trace generating functionsIrreducibles representationsMultiplicitiesKoszulity propertyMATEMATICA::ALGEBRAÁlgebras associadas a grafos orientados em níveis e a propriedade da KoszulidadeAlgebras associated to layered directed graphs and Koszulity propertyTese