Banca de DEFESA: ANA BEATRIZ GOMES DA SILVA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : ANA BEATRIZ GOMES DA SILVA
DATE: 30/08/2023
TIME: 11:00
LOCAL: Ambiente Virtual
TITLE:

Z2-gradings of the Grassmann algebra: construction, PI-equivalence, isomorphisms

KEY WORDS:

Grassmann algebra; Z2-gradings; Automorphisms

PAGES: 65
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUBÁREA: Álgebra
SUMMARY:

The focus of our dissertation is to develope a study on the Z2-gradings of the infinite-
dimensional Grassmann algebra E. The homogeneous Z2-gradings and their Z2-grade identities

are already well known in the literature, see (VINCENZO; SILVA, 2009), (CENTRONE, 2011) and
(GONÇALVES, 2018). Nevertheless, the construction of non-homogeneous 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. In a second moment, 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,
refuting the conjecture presented in (GUIMARÃES; KOSHLUKOV, 2023).

COMMITTEE MEMBERS:
Externo à Instituição - LUCIO CENTRONE
Presidente - 1143007 - ALAN DE ARAUJO GUIMARAES
Externo à Instituição - CLAUDEMIR GOMES BARBOSA MOREIRA - UNICAMP
Interna - 1143603 - ELAINE GOUVEA PIMENTEL