Álgebras associadas a grafos orientados em níveis e a propriedade da Koszulidade
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Data
2014-11-20
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Universidade Federal de Goiás
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:
Descrição
Citação
VASCONCELOS, 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.