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 -dimensional -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 -dimensional nilpotent associative algebras. In particular, it has been proven that this variety has irreducible components and rigid algebras.
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