Four-Dimensional Algebras А4 With Radical R(A4) Of Dimension 0 And 1"

Abstract

The structure constants of the algebra A4 define, in four-dimensional affine space, a system of curvilinear coordinates with constant connection coefficients. The study of curvilinear coordinates with constant connection coefficients is related to the study and classification of commutative and associative algebras А4. Therefore, this work considers the classification of commutative and associative algebras A4 with radical R(A4) of dimension 0 and 1.