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arXiv · 1601.00554

Asymptotically optimal $k$-step nilpotency of quadratic algebras and the Fibonacci numbers

Natalia Iyudu·Stanislav Shkarin
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Abstract

It follows from the Golod--Shafarevich theorem that if R is an associative algebra given by n generators and $d<\frac{n^2}{4}\cos^{-2}(\fracπ{k+1})$ quadratic relations, then R is not k-step nilpotent. We show that the above estimate is asymptotically optimal, and establish number of related results. For example, we show that for any k this estimate is attained for ifinitely many n.

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Natalia Iyudu, Stanislav Shkarin. 2016-01-04. Asymptotically optimal $k$-step nilpotency of quadratic algebras and the Fibonacci numbers. https://arxiv.org/abs/1601.00554

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