The proof of the Kontsevich periodicity conjecture on noncommutative birational transformations.

DOI10.1215/00127094-3146603zbMath1334.16028arXiv1305.1965OpenAlexW1837322850WikidataQ122943232 ScholiaQ122943232MaRDI QIDQ902250

Stanislav Shkarin, Natalia K. Iyudu

Publication date: 7 January 2016

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.1965

zbMATH Keywords

free fieldsKontsevich conjectureCremona transformationsbirational dynamicsHadamard matrix productmatrices over noncommutative ringsnoncommutative birational involutionsnoncommutative identities

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Rings arising from noncommutative algebraic geometry (16S38) Endomorphism rings; matrix rings (16S50) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Cluster algebras (13F60) Associative rings of fractions and localizations (16S85)

Related Items (2)

Birational rowmotion on a rectangle over a noncommutative ring ⋮ Re-factorising a QRT map

Cites Work

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• A short proof of Kontsevich's cluster conjecture.
• Growth and integrability in the dynamics of mappings
• Quasideterminants
• Algebraicity of the zeta function associated to a matrix over a free group algebra
• Dynamics of complexity of intersections
• ON THE CONSTRUCTION OF THE FREE FIELD

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