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.

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

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Cited by in corpus (1)

• Non-associative algebraic structures: classification and structure