Elements of homometric 2-algebra and their representations

Abstract

This paper presents a scientific proposal on a new algebra, the Homometric 2-Algebra, whose product of vectors is called homometric vector 2-product, which transforms two multiplicative vectors of a given vector space into an axial vector of this same vector space, essentially characterized as an axial vector simultaneously orthogonal to the two multiplicative vectors. This homometric vector 2-product fulfills other fundamental properties such as antisymmetry, Lagrange identity, and Jacobi identity is not valid, in general. Moreover, this homometric vector 2-product admits the Gibbs and Heaviside vector product as a particular case that occurs in three-dimensional real vector spaces, which allows us to state that the Homometric 2-Algebra is a natural generalization of the Gibbs and Heaviside algebra for n-dimensional spaces and for the body of complex numbers. Thus, this paper aims, in general, to analyze the scientific foundations of Homometric 2-Algebra, its properties, functionalities and some applications in financial management, in the context of homometric vector spaces. To this end, research of theoretical-exploratory typology was used, which employs the logical-deductive method for the conceptualization of Homometric 2-Algebra, relating it to other algebraic structures, while its main scientific foundations and some applications in the context of financial management are identified.