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

Mikhail V. IgnatyevSamara National Research University, Samara, RussiaIvan KaygorodovCentro de Matemática e Aplicações, Universidade da Beira Interior, Covilhã, PortugalYury PopovSaint Petersburg State University, Saint Petersburg, Russia
2021en
ABI

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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Cited by 40 references