Banca de QUALIFICAÇÃO: JESSICA STEFANNY SOUSA DE LIMA

Uma banca de QUALIFICAÇÃO de MESTRADO foi cadastrada pelo programa.
STUDENT : JESSICA STEFANNY SOUSA DE LIMA
DATE: 09/09/2021
TIME: 10:00
LOCAL: Ambiente Virtual
TITLE:

Automorphisms of the category of free associative and commutative algebras with unit

KEY WORDS:

Polynomial algebra; verbal operation; automorphisms of the category of polynomial algebras.

PAGES: 70
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

In Universal Algebraic Geometry over a variety of algebras, the group of
automorphisms of the category of free finitely generated algebras plays an important
role. It turns out that for the wide class of varieties,  an automorphism of the category of
free finitely generated algebras can be decomposed to the product of an inner
automorphism and a strongly stable automorphism. The method of verbal operations
provides a machinery to calculate the group of strongly stable automorphisms.

In  the present work, we deal with the variety of associative and commutative algebras
with unit over an infinite field of zero characteristic. Note that free finitely generated
algebras in this variety are exactly algebras of commutative and associative polynomials
with unit over an finite set of variables.
The main goal of this thesis is to investigate automorphisms of the category of free
finitely generated algebras in this variety.  In particular,  applying the method of verbal
operations we get description of strongly stable automorphisms of the category under
consideration.

BANKING MEMBERS:
Presidente - 2147844 - ARKADY TSURKOV
Interno - 1143007 - ALAN DE ARAUJO GUIMARAES
Interno - 2340150 - ALEXEY KUZMIN
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Externa ao Programa - 2425364 - ELENA ALADOVA