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Optimal 5-step nilpotent quadratic algebras

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Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalJournal of Algebra
Publication statusPublished - 15 Aug 2014


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 inverted right perpendicularn(2)/3inverted left perpendicular homogeneous quadratic relations such that R is 5-step nilpotent. (C) 2014 Published by Elsevier Inc.

    Research areas

  • Quadratic algebras, Golod-Shafarevich theorem, Hilbert series, Anick's conjecture, Nilpotency index, HILBERT SERIES

ID: 16662150