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Asymptotically optimal $k$-step nilpotency of quadratic algebras and the Fibonacci numbers
- Source :
- Combinatorica, V 37 (2017), n3, p.465-479
- Publication Year :
- 2016
-
Abstract
- It follows from the Golod--Shafarevich theorem that if R is an associative algebra given by n generators and $d<\frac{n^2}{4}\cos^{-2}(\frac{\pi}{k+1})$ quadratic relations, then R is not k-step nilpotent. We show that the above estimate is asymptotically optimal, and establish number of related results. For example, we show that for any k this estimate is attained for ifinitely many n.<br />Comment: to appear in Combinatorica
- Subjects :
- Mathematics - Rings and Algebras
17A45, 16A22
Subjects
Details
- Database :
- arXiv
- Journal :
- Combinatorica, V 37 (2017), n3, p.465-479
- Publication Type :
- Report
- Accession number :
- edsarx.1601.00554
- Document Type :
- Working Paper