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arXiv · 2103.01036

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

Mikhail Ignatyev·Ivan Kaygorodov·Yury Popov
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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.

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Mikhail Ignatyev, Ivan Kaygorodov, Yury Popov. 2021-09-01. The geometric classification of $2$-step nilpotent algebras and applications. https://doi.org/10.1007/s13163-021-00411-0

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