Banca de QUALIFICAÇÃO: LIGIA DANIELLY ROCHA DOS SANTOS

Uma banca de QUALIFICAÇÃO de MESTRADO foi cadastrada pelo programa.
STUDENT : LIGIA DANIELLY ROCHA DOS SANTOS
DATE: 07/11/2024
TIME: 14:30
LOCAL: Sala de seminários do ccet, dmat
TITLE:

On PI-equivalence and isomorphism of superalgebras (and algebras with involution) of the Grassmann algebra

KEY WORDS:

involutions; superalgebras, Grassmann algebra, PI-equivalence, isomorphism.

PAGES: 80
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUBÁREA: Álgebra
SPECIALTY: Álgebra Comutativa
SUMMARY:

Let $F$ be a field of characteristic different from two, $E$ the Grassmann algebra of an infinite dimensional $F$-vector space $L$, and $\mathrm{Aut}^{\ast}(E)$ the group of automorphisms and anti-automorphisms of $E$. Given $\varphi\in \mathrm{Aut}^{\ast}(E)$ such that $\varphi^2=\mathrm{Id}$, we denote by $E_{\varphi}$ (or $(E,\varphi)$) the induced superalgebra (or algebra with involution), depending on whether $\varphi$ is an automorphism or anti-automorphism. Under certain conditions on $\varphi$, we classify these structures up to isomorphism. Moreover, when $\varphi_{1}$ and $\varphi_{2}$ are homogeneous (i.e., $\varphi_{1}(L)=\varphi_{2}(L)=L$), we provide conditions for the induced structures to be isomorphic. As a consequence, we show that, in general, PI-equivalence of algebras with involution on $E$ does not imply isomorphism. Moreover, we prove that the homogeneous superalgebras on $E$ are determined up to isomorphism by its graded polynomial identities if and only if the dimension of $L$ is enumerable.

COMMITTEE MEMBERS:
Presidente - 1143007 - ALAN DE ARAUJO GUIMARAES
Externo ao Programa - 2340150 - ALEXEY KUZMIN - UFRNExterno ao Programa - 2147844 - ARKADY TSURKOV - UFRNExterno ao Programa - 3362695 - JOSE VICTOR GOMES TEIXEIRA - UFRN