Abstract
By the Golod–Shafarevich theorem, an associative algebra $R$ given by $n$ generators and $<n^2/3$ homogeneous quadratic relations is not 5step 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 $\lceil n^2/3\rceil$ homogeneous quadratic relations such that $R$ is 5step nilpotent.
Original language  English 

Pages (fromto)  114 
Number of pages  14 
Journal  Journal of Algebra 
Volume  412 
Early online date  17 May 2014 
DOIs  
Publication status  Published  15 Aug 2014 
Keywords
 quadratic algebras, Anick's conjecture, GolodShafarevich theorem
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Profiles

Stanislav Shkarin
Person: Academic