Álgebras com estruturas adicionais de crescimento polinomial
Ano de defesa: | 2021 |
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Autor(a) principal: | |
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Banca de defesa: | |
Tipo de documento: | Dissertação |
Tipo de acesso: | Acesso aberto |
Idioma: | por |
Instituição de defesa: |
Universidade Federal de Minas Gerais
Brasil ICX - DEPARTAMENTO DE MATEMÁTICA Programa de Pós-Graduação em Matemática UFMG |
Programa de Pós-Graduação: |
Não Informado pela instituição
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Departamento: |
Não Informado pela instituição
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País: |
Não Informado pela instituição
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Palavras-chave em Português: | |
Link de acesso: | http://hdl.handle.net/1843/51007 |
Resumo: | The classic Kemer's Theorem, established in $1979$, states that a variety of algebras $V$ has polynomial growth if, and only if, $UT_2, \mathcal{G} \notin V$. The Kemer’s caracterization was extended to algebras with additional structures by other authors. In $2001$, Giambruno and Mishchenko proved that a necessary and sufficient condition to have $V$ as a $*$-variety of polynomial growth is excluding the $*$-algebras $D_*$ and $M_*$ from $V$. In the same year, Giambruno, Mishchenko and Zaicev characterized varieties of superalgebras with polynomial growth by the exclusion of five superalgebras from the variety of superalgebras, which are: $UT_2$, $\mathcal{G}$, $UT_2^{gr}$, $\mathcal{G} ^{gr}$ and $D^{gr}$. Finally, in $2016$, Giambruno, dos Santos and Vieira proved that it is necessary and sufficient to exclude the $*$-superalgebras $D_*$, $M_*$, $D^{gr}$, $D^{gri}$ and $M^{gri}$ from a variety of $*$-superalgebras in order to have polynomial growth. The main purpose of this dissertation is to present the previous characterizations, giving proofs with updated language developed in PI-theory in the last years. |