Optimal 5-step nilpotent quadratic algebras

Natalia Iyudu*, Stanislav Shkarin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalJournal of Algebra
Volume412
DOIs
Publication statusPublished - 15 Aug 2014

Keywords / Materials (for Non-textual outputs)

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

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