Classificação de álgebras reais de Clifford e de raízes de polinômios com coeficientes de álgebras de R4

Abstract

Clifford Algebras are an abstract construct related to bilinear vector spaces, whilst Polynomials with R^4 coefficients are a generalization of the study of polynomials with complex coefficients. The study of tensor product and tensor algebras is first presented as a theoretical base to be build upon. The definition of a Clifford Algebra over the real numbers and its universal property are studied. The classification of Clifford Algebras related to real finite-dimensional vector spaces is presented with the use of the Periodicity Theorem. Then the presentation eight algebras defined in R^4 is done. The classification of roots from one sided polynomials with quartenionic coefficients is first presented, followed by the one-sided polynomials over noncommutative algebras of R^4, and then by the two-sided quaternionic polynomial’s case.