Asymptotically optimal \(k\)-step nilpotency of quadratic algebras and the Fibonacci numbers

DOI10.1007/S00493-016-3009-6zbMath1399.16070arXiv1601.00554OpenAlexW2963901543MaRDI QIDQ682120

Stanislav Shkarin, Natalia K. Iyudu

Publication date: 13 February 2018

Published in: Combinatorica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.00554

zbMATH Keywords

Fibonacci numbersnilpotent algebrasdefining relationsquadratic algebrasGolod-Shafarevich theorem

Mathematics Subject Classification ID

Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Quadratic and Koszul algebras (16S37)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Non-commutative graded algebras and their Hilbert series
• How to recognize a Fibonacci number?
• Finite dimensional semigroup quadratic algebras with the minimal number of relations
• The entropy of graded algebras
• Graphs of relations and Hilbert series.
• The Golod-Shafarevich inequality for Hilbert series of quadratic algebras and the Anick conjecture
• Konstruktion nilpotenter assoziativer Algebren mit wenig Relationen
• An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension
• A Proof of Dilworth's Chain Decomposition Theorem
• SOME OPEN PROBLEMS IN THE THEORY OF INFINITE DIMENSIONAL ALGEBRAS

This page was built for publication: Asymptotically optimal \(k\)-step nilpotency of quadratic algebras and the Fibonacci numbers