The Golod-Shafarevich inequality for Hilbert series of quadratic algebras and the Anick conjecture

DOI10.1017/S030821051099999XzbMath1239.16030arXiv1007.3944OpenAlexW2064454985WikidataQ123117422 ScholiaQ123117422MaRDI QIDQ3006522

Stanislav Shkarin, Natalia K. Iyudu

Publication date: 20 June 2011

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.3944

zbMATH Keywords

finite-dimensional algebrasHilbert seriesnumbers of generatorsquadratic algebrasnumbers of relationsGolod-Shafarevich theoremquadratic relationsAnick conjectureVershik conjecture

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Growth rate, Gelfand-Kirillov dimension (16P90) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Semigroup rings, multiplicative semigroups of rings (20M25) Quadratic and Koszul algebras (16S37)

Related Items (5)

GOLOD–SHAFAREVICH GROUPS: A SURVEY ⋮ Optimal 5-step nilpotent quadratic algebras ⋮ Growth, entropy and commutativity of algebras satisfying prescribed relations. ⋮ Asymptotically optimal \(k\)-step nilpotency of quadratic algebras and the Fibonacci numbers ⋮ Finite dimensional semigroup quadratic algebras with the minimal number of relations

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