Modelos Computacionais para Verificação de Identidades Polinomiais em Álgebras de Matrizes com entradas na Álgebra de Grassmann
DOI:
https://doi.org/10.5540/tema.2018.019.03.489Keywords:
PI-álgebras, Maple, Computação Algébrica, Identidades Polinomiais Fracas.Abstract
Nesse trabalho apresentamos uma abordagem computacional para tratar das álgebras que satisfazem identidades polinomiais. Mais precisamente, utilizamos o software Maple para verificar e identificar identidades polinomiais das álgebras de matrizes com entradas na álgebra de Grassmann E, em especial a álgebra Mk,l(E), a qual Di Vincenzo e La Scala apresentam resultados interessantes quando k=l=1, usando a noção de identidades polinomiais fracas. Foram criados alguns procedimentos em Maple para adequar o produto das matrizes segundo as propriedades de $E$, sendo esta uma álgebra não comutativa. O software Maple apresenta algumas funções previamente implementadas que permitem trabalhar com tais propriedades, porém, o tempo de processamento é consideravelmente maior em comparação com algumas das funções que implementamos. Finalizamos com estudo da conjectura dada por Kemer a cerca do grau mínimo do polinômio standard para a álgebra Mn(E).References
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