Please use this identifier to cite or link to this item: http://hdl.handle.net/1843/EABA-B55PUP
Type: Tese de Doutorado
Title: On the factorability of T2-ideals of minimal supervarieties and a special class of minimal superalgebras
Authors: Danilo Vilela Avelar
First Advisor: Viviane Ribeiro Tomaz da Silva
First Referee: Ana Cristina Vieira
Second Referee: Rafael Bezerra dos Santos
Third Referee: Ivan Chestakov
metadata.dc.contributor.referee4: Plamen Emilov Koshlukov
Abstract: Nesta tese iremos lidar com o caso (...)-graduado. A saber, nosso foco será em superálgebras minimais e em supervariedades minimais.
Abstract: Let F be an algebraically closed field of characteristic zero. In this thesis, we describe necessary and suficient conditions for the factorability of T2-ideals of minimal supervarieties of a fixed superexponent. In light of the characterization of the minimal supervarieties of a fixed superexponent given by Di Vincenzo, da Silva and Spinelli, our main strategy is describing the factorability of the T2-ideals of the upper block triangular matrix algebras (...) equipped with elementary Z2-gradings, where A1, . An are finite-dimensional simple superalgebras. In addition, we classify, up to Z2-graded isomorphism, the minimal superalgebras (...). We also state that the concept of Z2-regularity establishes a nice connection between the factorability of the T2-ideal of (...) and the number of isomorphism classes of (...). As another approach, we define an r-special minimal superalgebra as a minimal superalgebra A with semisimple part (...) such that, for one index (...), whereas for all remaining indices (...) We obtain necessary and suficient conditions for the supervariety generated by A to be minimal. Moreover, we classify, up to Z2-graded isomorphism, the r-special minimal superalgebras. In particular, we prove that any r-special minimal superalgebra is a quotient of an appropriate subalgebra of an upper block triangular matrix algebra, with respect to an elementary Z2-grading. As a consequence of our results, we state that the r-special minimal superalgebras are determined, up to Z2-graded isomorphism, by the Z2-graded polynomial identities satisfied by them.
Subject: Matemática
Superálgebras
Isomorfismos (Matematica)
Supervariedades (Matematica)
language: Inglês
Publisher: Universidade Federal de Minas Gerais
Publisher Initials: UFMG
Rights: Acesso Aberto
URI: http://hdl.handle.net/1843/EABA-B55PUP
Issue Date: 22-Aug-2018
Appears in Collections:Teses de Doutorado

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