Generic verbally prime pi-algebras and their gk-dimensions

DOI10.1080/00927879308824632zbMath0816.16025OpenAlexW2133888588MaRDI QIDQ4696698

Allan Berele

Publication date: 29 June 1993

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879308824632

zbMATH Keywords

matrix algebrasGrassmann algebrasGelfand-Kirillov dimensionpolynomial identitiesgeneric algebrasrelatively free algebras\(T\)-idealsverbally prime PI-algebrasalgebras of generic matrices

Mathematics Subject Classification ID

Growth rate, Gelfand-Kirillov dimension (16P90) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Exterior algebra, Grassmann algebras (15A75) Semiprime p.i. rings, rings embeddable in matrices over commutative rings (16R20) Identities other than those of matrices over commutative rings (16R40)

Related Items (34)

Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action ⋮ Relatively free algebras of finite rank ⋮ Tensor product theorems in positive characteristic. ⋮ Graded identities for algebras with elementary gradings over an infinite field ⋮ Star-polynomial identities: computing the exponential growth of the codimensions ⋮ Polynomial identities of algebras in positive characteristic. ⋮ PI non-equivalence in positive characteristic. ⋮ On the factorization of \(T_G\)-ideals of graded matrix algebras ⋮ On the polynomial identities of the algebra \(M_{11}(E)\). ⋮ On the *-polynomial identities of \(M_{1,1}(E)\). ⋮ Hilbert series of \(T\)-spaces ⋮ \(Y\)-proper graded cocharacters of the algebra \(UT_m(F)\) of \(m \times m\) upper triangular matrices over \(F\) ⋮ Denominators for one variable Poincaré series of generic matrices ⋮ Bounds on colength and maximal multiplicity sequences. ⋮ On the growth of graded polynomial identities of ⋮ GK dimension of the relatively free algebra for \(sl_2\) ⋮ The GK dimension of relatively free algebras of PI-algebras ⋮ Maximal multiplicities in cocharacter sequences. ⋮ The Gelfand-Kirillov dimension of the universal algebras of \(M_{a,b}(E)\otimes E\) in positive characteristic. ⋮ ℤ₂-Graded Gelfand–Kirillov dimension of the Grassmann algebra ⋮ Graded identities for T-prime algebras over fields of positive characteristic ⋮ GRADED IDENTITIES AND PI EQUIVALENCE OF ALGEBRAS IN POSITIVE CHARACTERISTIC ⋮ Classification theorems for verbally semiprime algebras ⋮ Polynomial identities for graded tensor products of algebras. ⋮ On PI-algebras with additional structures: rationality of Hilbert series and Specht's problem ⋮ PI (non)equivalence and Gelfand-Kirillov dimension in positive characteristic. ⋮ The graded Gelfand--Kirillov dimension of verbally prime algebras ⋮ T-ideals and superAzumaya algebras ⋮ Minimal varieties of associative algebras and transcendental series ⋮ Powers of standard identities satisfied by verbally prime algebras ⋮ Graded identities for tensor products of matrix (super)algebras over the Grassmann algebra ⋮ A NOTE ON GRADED GELFAND–KIRILLOV DIMENSION OF GRADED ALGEBRAS ⋮ Minimal varieties of algebras of exponential growth ⋮ Minimal varieties of algebras of exponential growth.

Cites Work

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• Homogeneous polynomial identities
• Cocharacters of \(\mathbb Z/2\mathbb Z\)-graded algebras
• Algebras satisfying a Capelli identity
• Free ideal rings
• VARIETIES AND $ Z_2$-GRADED ALGEBRAS

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