Um estudo sobre álgebras associadas a alguns grafos orientados em níveis
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2017-08-28
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Universidade Federal de Goiás
Resumo
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.
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DIRINO, K. A. Um estudo sobre álgebras associadas a alguns grafos orientados em níveis. 2017. 76 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2017.