Banca de DEFESA: JOSÉ VICTOR GOMES TEIXEIRA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : JOSÉ VICTOR GOMES TEIXEIRA
DATE: 05/07/2021
TIME: 13:00
LOCAL: Ambiente Virtual
TITLE:

Some results about groups of outer automorphisms of categories of finitely generated nilpotent free algebras

KEY WORDS:

Universal algebraic geometry, category theory, strongly stable automorphisms, nilpotent linear algebras

PAGES: 60
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

This dissertation has as objective the study of the group $\mathfrak{A}/\mathfrak{Y\cong S/S\cap Y}$ for category of finitely generated free algebras in the variety of $n$-nilpotent linear algebras. There exists a conjecture that for every $n$ we have $\mathfrak{A}/\mathfrak{Y\cong }k^{\ast }\rtimes Autk$. This conjecture was proved for n=3,4,5. We tried to prove this conjecture for every n. The problem was not completely resolved, but some progress has been made. The parameterization of the group $\mathfrak{S}$ has been set. The decomposition of the group $\mathfrak{H}$ associated with this parameterization was proved. One of the algorithms has been developed that can prove that $\mathfrak{H}\leq $ $\mathfrak{Y}$. After this, problem will be resolved. Complete problem solving can be the topic of a doctoral dissertation. The study of the group $\mathfrak{A}/\mathfrak{Y}$ for every variety is very important in the area of Universal Algebraic Geometry, because this group gives us the possible differences between geometric and automorphic equivalence of algebras of this variety.

BANKING MEMBERS:
Interno - 2340150 - ALEXEY KUZMIN
Presidente - 2147844 - ARKADY TSURKOV
Externo à Instituição - EVGENY PLOTKIN - Bar-Ilan