The GK dimension of relatively free algebras of PI-algebras

DOI10.1016/j.jpaa.2018.10.005zbMath1461.16024OpenAlexW2895159773MaRDI QIDQ1730857

Lucio Centrone

Publication date: 6 March 2019

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2018.10.005

zbMATH Keywords

Gelfand-Kirillov dimensiongraded polynomial identitiesgeneric matrix algebras

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Growth rate, Gelfand-Kirillov dimension (16P90) Graded rings and modules (associative rings and algebras) (16W50) (T)-ideals, identities, varieties of associative rings and algebras (16R10)

Related Items (5)

Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action ⋮ Gelfand-Kirillov dimension of bicommutative algebras ⋮ \(Y\)-proper graded cocharacters of the algebra \(UT_m(F)\) of \(m \times m\) upper triangular matrices over \(F\) ⋮ Varieties of null-filiform Leibniz algebras under the action of Hopf algebras ⋮ On PI-algebras with additional structures: rationality of Hilbert series and Specht's problem

Cites Work

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• Kemer's theory for \(H\)-module algebras with application to the PI exponent
• Graded polynomial identities and codimensions: computing the exponential growth.
• Homogeneous polynomial identities
• Cocharacters of \(\mathbb Z/2\mathbb Z\)-graded algebras
• Codimensions of products and of intersections of verbally prime T-ideals
• Group-graded algebras with polynomial identity
• On codimension growth of finitely generated associative algebras
• Exponential codimension growth of PI algebras: an exact estimate
• Monomial algebras
• A characterization of P. I. algebras with bounded multiplicities of the cocharacters
• Polynomial identities on superalgebras and exponential growth
• Group graded PI-algebras and their codimension growth.
• On the graded identities of \(M_{1,1}(E)\)
• Minimal varieties of algebras of exponential growth.
• Representability and Specht problem for \(G\)-graded algebras.
• Semigroup graded algebras and graded PI-exponent
• Applications of Belov's theorem to the cocharacter sequence of p.i. algebras.
• Representations of permutation groups. Part I
• Z_P-CODIMENSIONS OF Z_P-IDENTITIES OF GRASSMANN ALGEBRA
• Multialternating graded polynomials and growth of polynomial identities
• Graded polynomial identities and exponential growth
• Identities of PI-Algebras Graded by a Finite Abelian Group
• The graded Gelfand--Kirillov dimension of verbally prime algebras
• A NOTE ON GRADED GELFAND–KIRILLOV DIMENSION OF GRADED ALGEBRAS
• On the codimension growth of 𝐺-graded algebras
• VARIETIES AND $ Z_2$-GRADED ALGEBRAS
• Identities of associative algebras
• $\mathbf {Z}_n$-graded polynomial identities of the full matrix algebra of order $n$
• Cocharacters, Codimensions and Hilbert Series of the Polynomial Identities for 2 × 2 Matrices with Involution
• Cocharacters of g-graded algebras
• Generic verbally prime pi-algebras and their gk-dimensions
• Group Gradings on Matrix Algebras
• Graded Polynomial Identities for Tensor Products by the Grassmann Algebra
• Identities of graded algebras and codimension growth
• ℤ₂-Graded Gelfand–Kirillov dimension of the Grassmann algebra
• Amitsur’s conjecture for polynomial 𝐻-identities of 𝐻-module Lie algebras
• The Gel'fand-Kirillov dimension of relatively free associative algebras

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