Guimarães, Alan de AraújoSantos, Lígia Danielly Rocha dos2025-03-202025-03-202025-01-24SANTOS, Lígia Danielly Rocha dos. Involuções da álgebra de Grassmann: um estudo sobre *- polinômios centrais, *-identidades e *-isomorfismos. Orientador: Dr. Alan de Araújo Guimarães. 2025. 82f. Dissertação (Mestrado em Matemática Aplicada e Estatística) - Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Natal, 2025.https://repositorio.ufrn.br/handle/123456789/63122Let K be a field of characteristic distinct from two, E be the Grassmann algebra of a K-vector space with infinite and countable base L and let φ be any involution. Based on the article (CENTRONE; GONCALVES; SILVA, 2020), we present generating sets for the ∗-polynomial identities and ∗-central polynomials of the Grassmann algebra, with a strong distinction between the cases char(K) = 0 and char(K) > 2. According to (DINIZ; GUIMARÃES; ROCHA, 2024), when φ satisfies certain conditions, we show that there is homogeneous involution φl (i.e., φl(L) = L) such that (E, φ) and (E, φl) are ∗-isomorphic. Additionally, we present certain necessary and sufficient condition for two homogeneous involutions to produce ∗-isomorphic structures. As a consequence, we obtain examples of algebras that are ∗-PI-equivalent and that are not ∗-isomorphic algebras.Acesso AbertoÁlgebra de GrassmannInvoluções*-identidades*-isomorfismos*-polinômios centraismasterThesisCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA