Article ID Journal Published Year Pages File Type
4602187 Linear Algebra and its Applications 2009 10 Pages PDF
Abstract

We establish the equivalence between the problem of existence of associative bilinear forms and the problem of solvability in commutative power-associative finite-dimensional nil-algebras. We use the tensor product to find sufficient and necessary conditions to assure the existence of associative bilinear forms in an algebra A. The result gives us an algorithm to describe the space of associative bilinear forms for an algebra when its constants of structure γi,j,k for i,j,k=1,…,n are known.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory