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arXiv · 1806.07009

Classification of bilinear maps with radical of codimension 2

Antonio Jesús Calderón·Amir Fernández Ouaridi·Ivan Kaygorodov
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Abstract

Let ${\mathbb V}$ be an $n$-dimensional linear space over an algebraically closed base field. We provide a classification, up to equivalence, of all of the bilinear maps $f:{\mathbb V} \times {\mathbb V} \to {\mathbb V}$ such that $dim(rad(f)) =n-2$. This is equivalent to give a complete classification (up to isomorphism) of all $n$-dimensional algebras with annihilator of dimension $n-2$ or, in other words, a classification of the annihilator extensions of all $2$-dimensional algebras.

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Antonio Jesús Calderón, Amir Fernández Ouaridi, Ivan Kaygorodov. 2018-06-19. Classification of bilinear maps with radical of codimension 2. https://doi.org/10.1080/03081087.2020.1849001

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