Banca de DEFESA: LIGIA DANIELLY ROCHA DOS SANTOS

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : LIGIA DANIELLY ROCHA DOS SANTOS
DATE: 24/01/2025
TIME: 10:00
LOCAL: Sala de seminários da Matemática, CCET
TITLE:

involutions of Grassmann Algebra: A Study on *-Central Polynomials, *-Identities, and * Isomorphisms

KEY WORDS:

i Grassmann algebra, involutions, *-identities, *-isomorphisms, *-central polynomials

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

Let K be a field with characteristics different from two, E be the Grassmann algebra of a K-vector space with infinite and enumerable base L and φ be any involution. Based on the article (CENTRONE; GONCALVES; SILVA, 2020a), we present generating sets for the ∗ polynomial identities and ∗-central polynomials of Grassmann algebra, with a strong distinction between the cases char(K) = 0 and char(K) > 2. According to (DINIZ; GUIMARÃES; ROCHA), 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. Furthermore, we present a necessary and sufficient condition for two homogeneous involutions to produce ∗-isomorphic structures. As a consequence, we obtained examples of ∗-PI-equivalent and not ∗-isomorphic algebras.

COMMITTEE MEMBERS:
Presidente - 1143007 - ALAN DE ARAUJO GUIMARAES
Externo ao Programa - 2340150 - ALEXEY KUZMIN - nullExterno ao Programa - 2147844 - ARKADY TSURKOV - nullExterno à Instituição - DAVID LEVI DA SILVA MACÊDO
Externo à Instituição - DIOGO DINIZ PEREIRA DA SILVA E SILVA
Externo ao Programa - 3362695 - JOSE VICTOR GOMES TEIXEIRA - nullExterna à Instituição - LAISE DIAS ALVES ARAÚJO
Externo à Instituição - PEDRO HENRIQUE MARTINS DE MORAIS