Classificação e identidades polinomiais de álgebras de Jordan bidimensionais

Abstract

In this work we classify the two-dimensional Jordan algebras over a field K of characteristic different from 2. As a consequence, we prove that there exists, up to isomorphism, a unique two-dimensional non-associative Jordan algebra over K, such an algebra can be generalized to an algebra of arbitrary dimension, maintaining the algebraic properties that are fundamental in our study. When K, in addition to having characteristic different from 2, is an infinite field, we determine a finite basis for the T-ideals of the polynomial identities of each of these algebras obtained in the classification and also their codimension sequence. Furthermore, when K has characteristic 0, we determine the cocharacter sequence of these algebras.