Z2-graduações da álgebra de Grassmann: construção, PI-equivalência e isomorfismos
The focus of our dissertation is to develope a study on the Z2-gradings of the infinitedimensional Grassmann algebra E. The homogeneous Z2-gradings and their Z2-graded identities are already well known in the literature, see (VINCENZO; SILVA, 2009), (CENTRONE, 2011) e (GONÇALVES, 2018). Nevertheless...
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| Formato: | Dissertação |
| Idioma: | pt_BR |
| Publicado em: |
Universidade Federal do Rio Grande do Norte
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| Endereço do item: | https://repositorio.ufrn.br/handle/123456789/55627 |
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| Resumo: | The focus of our dissertation is to develope a study on the Z2-gradings of the infinitedimensional Grassmann algebra E. The homogeneous Z2-gradings and their Z2-graded identities are already well known in the literature, see (VINCENZO; SILVA, 2009), (CENTRONE, 2011) e (GONÇALVES, 2018). Nevertheless, the construction of nonhomogeneous Z2-gradings demands the use of the duality between these structures and
automorphisms of order ≤ 2 acting on E. Through this, we will study the non-homogeneous
Z2-gradings, producing results on their construction. Next, we will investigate under what
conditions a non-homogeneous Z2-grading is isomorphic to the canonical Z2-grading of
E. Finally, we will provide a Z2-grading on E in which there is no non-zero element
of the space L homogeneous, giving a negative answer to the conjecture presented in
(GUIMARÃES; KOSHLUKOV, 2023). |
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