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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 |
Files in This Item:
File | Description | Size | Format | |
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tese_danilo.pdf | 739.87 kB | Adobe PDF | View/Open |
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