The geometric classification of $2$-step nilpotent algebras and applications

Abstract

We give a geometric classification of complex $n$-dimensional $2$-step nilpotent (all, commutative and anticommutative) algebras. Namely, has been found the number of irreducible components and their dimensions. As a corollary, we have a geometric classification of complex $5$-dimensional nilpotent associative algebras. In particular, it has been proven that this variety has $14$ irreducible components and $9$ rigid algebras.

Theorem C is corrected. arXiv admin note: text overlap with arXiv:2007.01829, arXiv:2001.00253

References in corpus (2)

• Canonical matrices of bilinear and sesquilinear forms
• The geometric classification of nilpotent algebras

Cited by in corpus (1)

• Non-associative algebraic structures: classification and structure