ABSTRACT
Let be an n-dimensional linear space over an algebraically closed base field. We provide a general method for classifying, up to equivalence, all bilinear maps
such that
, in case a classification of bilinear maps
when
is known. This is equivalent to giving a procedure to classify (up to isomorphism) all n-dimensional algebras with annihilator of dimension n−m from a given classification of m-dimensional algebras. As an example of application, we consider the case in which m = 2.
Acknowledgments
We would like to thank the referee for the detailed reading of this work and for the valuable suggestions to improve the same.
Table 2. Classification of 3-dimensional bilinear pairs with 1-dimensional radicals.
Table 3. Classification of 4-dimensional bilinear pairs with 2-dimensional radicals.
Table 4. Classification of 5-dimensional bilinear pairs with 3-dimensional radicals.
Disclosure statement
No potential conflict of interest was reported by the author(s).