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arXiv · 1512.08594

Optimal 5-step nilpotent quadratic algebras

Natalia Iyudu·Stanislav Shkarin
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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.

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Natalia Iyudu, Stanislav Shkarin. 2015-12-29. Optimal 5-step nilpotent quadratic algebras. https://arxiv.org/abs/1512.08594

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