Optimal 5-step nilpotent quadratic algebras
Rings and Algebras
2015-12-31 v1
Abstract
By the Golod--Shafarevich Theorem, an associative algebra R given by n generators and d<n^2/3 homogeneous quadratic relations is not 5-step nilpotent. We prove that this estimate is optimal. Namely, we show that for every positive integer n, there is an algebra R given by n generators and n^2/3 homogeneous quadratic relations such that R is 5-step nilpotent.
Keywords
Cite
@article{arxiv.1512.08594,
title = {Optimal 5-step nilpotent quadratic algebras},
author = {Natalia Iyudu and Stanislav Shkarin},
journal= {arXiv preprint arXiv:1512.08594},
year = {2015}
}