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Optimal 5-step nilpotent quadratic algebras
- Source :
- Journal of Algebra, v.412, 2014, p.1-14
- Publication Year :
- 2015
-
Abstract
- 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 n^2/3 homogeneous quadratic relations such that R is 5-step nilpotent.
- Subjects :
- Mathematics - Rings and Algebras
17A45, 16A22
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Algebra, v.412, 2014, p.1-14
- Publication Type :
- Report
- Accession number :
- edsarx.1512.08594
- Document Type :
- Working Paper