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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 language | English |
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Pages (from-to) | 1-14 |
Number of pages | 14 |
Journal | Journal of Algebra |
Volume | 412 |
DOIs | |
Publication status | Published - 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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