The graded Gelfand--Kirillov dimension of verbally prime algebras

DOI10.1080/03081087.2011.559636zbMath1248.16021OpenAlexW2040527757MaRDI QIDQ3104570

Lucio Centrone

Publication date: 14 December 2011

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2011.559636

zbMATH Keywords

Grassmann algebrasGelfand-Kirillov dimensiongraded polynomial identitiesgeneric matrix algebrasgraded PI-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) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Graded rings and modules (associative rings and algebras) (16W50) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Exterior algebra, Grassmann algebras (15A75)

Related Items (6)

Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action ⋮ On the growth of graded polynomial identities of ⋮ The GK dimension of relatively free algebras of PI-algebras ⋮ \(Y\)-proper graded cocharacters of upper triangular matrices of order \(m\) graded by the \(m\)-tuple \(\phi=(0,0,1,\ldots,m-2)\). ⋮ ℤ₂-Graded Gelfand–Kirillov dimension of the Grassmann algebra ⋮ On \(\mathbb Z_2\)-graded identities of \(UT_2(E)\) and their growth.

Cites Work

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• Cocharacters of \(\mathbb Z/2\mathbb Z\)-graded algebras
• Representations of permutation groups. Part I
• $\mathbf {Z}_n$-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
• GRADED IDENTITIES AND PI EQUIVALENCE OF ALGEBRAS IN POSITIVE CHARACTERISTIC
• Generic verbally prime pi-algebras and their gk-dimensions
• Graded Polynomial Identities for Tensor Products by the Grassmann Algebra
• ALGEBRAS SATISFYING THE POLYNOMIAL IDENTITY [x₁,x₂[x₃,x₄,x₅]=0]

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