English

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

Rings and Algebras 2021-11-02 v2 Algebraic Geometry

Abstract

We give a geometric classification of complex nn-dimensional 22-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 55-dimensional nilpotent associative algebras. In particular, it has been proven that this variety has 1414 irreducible components and 99 rigid algebras.

Keywords

Cite

@article{arxiv.2103.01036,
  title  = {The geometric classification of $2$-step nilpotent algebras and applications},
  author = {Mikhail Ignatyev and Ivan Kaygorodov and Yury Popov},
  journal= {arXiv preprint arXiv:2103.01036},
  year   = {2021}
}

Comments

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