Growth of polynomial identities: is the sequence of codimensions eventually non-decreasing?

DOI10.1112/blms/bdu031zbMath1302.16015OpenAlexW2131026473MaRDI QIDQ5495348

Antonio Giambruno, Mikhail V. Zaicev

Publication date: 4 August 2014

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/blms/bdu031

zbMATH Keywords

PI algebrascodimension sequencesnonassociative algebrascodimension growthPI exponentscodimensions of T-ideals

Mathematics Subject Classification ID

Growth rate, Gelfand-Kirillov dimension (16P90) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Nonassociative algebras satisfying other identities (17A30) Free nonassociative algebras (17A50)

Related Items (16)

Codimension sequences and their asymptotic behavior ⋮ Regev's conjecture for algebras with Hopf actions ⋮ Central polynomials of algebras and their growth ⋮ Superalgebras: polynomial identities and asymptotics ⋮ Anomalies on codimension growth of algebras. ⋮ Star-polynomial identities: computing the exponential growth of the codimensions ⋮ Exponential growth of codimensions of identities of algebras with unity ⋮ Polynomial identities and algebraic combinatorics on words ⋮ Codimensions of algebras with additional structures ⋮ Identities on algebras and combinatorial properties of binary words ⋮ The theory of formal languages and identities of nonassociative algebras ⋮ Trace codimensions of algebras and their exponential growth ⋮ Asymptotics of graded codimension of upper triangular matrices ⋮ Star-fundamental algebras: polynomial identities and asymptotics ⋮ The polynomial part of the codimension growth of affine PI algebras ⋮ Eventually non-decreasing codimensions of *-identities

Cites Work

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• On codimension growth of finitely generated associative algebras
• Exponential codimension growth of PI algebras: an exact estimate
• An example of a variety of Lie algebras with a fractional exponent
• Codimensions of algebras and growth functions
• A sufficient condition for coincidence of lower and upper exponents of the variety of linear algebras
• Existence of identities in \(A \otimes B\)
• Asymptotic behaviour of codimensions of p. i. algebras satisfying Capelli identities

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