Detalhes bibliográficos
| Ano de defesa: |
2014 |
| Autor(a) principal: |
Vasconcelos, José Eder Salvador de
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| Orientador(a): |
Silva, Jhone Caldeira
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| Banca de defesa: |
Rodrigues, Paulo Henrique de Azevedo,
Lima, Aline de Souza,
Guerreiro, Marinês,
Lemos, Manoel José Machado Soares,
Castonguay, Diane |
| Tipo de documento: |
Tese
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| Tipo de acesso: |
Acesso aberto |
| Idioma: |
por |
| Instituição de defesa: |
Universidade Federal de Goiás
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| Programa de Pós-Graduação: |
Programa de Pós-graduação em Matemática (IME)
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| Departamento: |
Instituto de Matemática e Estatística - IME (RG)
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| País: |
Brasil
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| Palavras-chave em Português: |
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| Palavras-chave em Inglês: |
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| Área do conhecimento CNPq: |
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| Link de acesso: |
http://repositorio.bc.ufg.br/tede/handle/tede/4444
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Resumo: |
In 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: |
