Guimarães, Alan de AraújoSilva, Ana Beatriz Gomes da2023-12-052023-12-052023-08-30SILVA, Ana Beatriz Gomes da. Z2-graduações da álgebra de Grassmann: construção, PI-equivalência e isomorfismos. Orientador: Dr. Alan de Araújo Guimarães. 2023. 67f. Dissertação (Mestrado em Matemática Aplicada e Estatística) - Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Natal, 2023.https://repositorio.ufrn.br/handle/123456789/55627The 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).Acesso AbertoÁlgebra de GrassmannZ2-graduaçõesAutomorfismosmasterThesisCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA