Classification of bilinear maps with radical of codimension 2

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.

References in corpus (3)

• Classification of five-dimensional nilpotent Jordan algebras
• Nilpotent evolution algebras over arbitrary fields
• The classification of $n$-dimensional anticommutative algebras with $(n-3)$-dimensional annihilator

Cited by in corpus (16)

• The variety of $2$-dimensional algebras over an algebraically closed field
• The algebraic and geometric classification of nilpotent anticommutative algebras
• The algebraic and geometric classification of nilpotent Novikov algebras
• The algebraic and geometric classification of nilpotent bicommutative algebras
• The algebraic and geometric classification of nilpotent terminal algebras
• The algebraic classification of nilpotent algebras
• The algebraic classification of nilpotent Tortkara algebras
• One-generated nilpotent Novikov algebras
• Central extensions of 3-dimensional Zinbiel algebras
• The algebraic classification of nilpotent $\mathfrak{CD}$-algebras
• One-generated nilpotent bicommutative algebras
• Symmetric Zinbiel superalgebras
• The algebraic and geometric classification of antiassociative algebras
• The algebraic classification of nilpotent commutative $\mathfrak{CD}$-algebras
• The algebraic classification of nilpotent Novikov algebras
• The geometric classification of $2$-step nilpotent algebras and applications