Sobre polinômios centrais em uma e duas variáveis para M2(K) quando K é um corpo finito

Júlio César dos Reis

doi:10.22481/exon.v4i2.19476

Autores

Júlio César dos Reis Southwest Bahia State University

DOI:

https://doi.org/10.22481/exon.v4i2.19476

Palavras-chave:

polinˆomio central, matrizes, corpos finitos, T-espa¸co, pi-´algebra

Resumo

Sejam K um corpo finito com q elementos e M₂(K) a ´algebra das matrizes de ordem dois sobre K. Conhecemos alguns exemplos de polinˆomios centrais, mas a base dos polinˆomios centrais de M₂(K) ´e desconhecida. Neste artigo, exibimos um polinˆomio central c(x) em uma vari´avel para M₂(K) tal que todo polinˆomio central em uma vari´avel ´e um m´ultiplo de c(x). Tamb´em exibimos uma conjectura para a base dos polinˆomios centrais para M₂(K).

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