Polynomial identities with involution, superinvolutions and the Grassmann envelope

DOI10.1090/proc/13546zbMath1406.16021OpenAlexW2546948857MaRDI QIDQ2964017

Eli Aljadeff, Yakov Karasik, Antonio Giambruno

Publication date: 22 February 2017

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13546

zbMATH Keywords

involutionGrassmann algebrapolynomial identitysuperinvolution

Mathematics Subject Classification ID

Other kinds of identities (generalized polynomial, rational, involution) (16R50) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) (T)-ideals, identities, varieties of associative rings and algebras (16R10)

Related Items (26)

On the asymptotics of Capelli polynomials ⋮ On codimensions of algebras with involution ⋮ Graded polynomial identities as identities of universal algebras ⋮ Graded linear maps on superalgebras ⋮ Star-polynomial identities: computing the exponential growth of the codimensions ⋮ The exponent for superalgebras with superinvolution ⋮ On central polynomials and codimension growth ⋮ Identities and central polynomials with involution for the Grassmann algebra ⋮ Deforming algebras with anti-involution via twisted associativity ⋮ Graded group actions and generalized \(H\)-actions compatible with gradings ⋮ On multiplicities of cocharacters for algebras with superinvolution ⋮ Codimensions of star-algebras and low exponential growth ⋮ Star-fundamental algebras: polynomial identities and asymptotics ⋮ Some characterizations of algebras with involution with polynomial growth of their codimensions ⋮ On the factorability of the ideal of \(\ast\)-graded polynomial identities of minimal varieties of PI \(\ast\)-superalgebras ⋮ Distinguishing simple algebras by means of polynomial identities ⋮ Superalgebras with involution or superinvolution and almost polynomial growth of the codimensions ⋮ Minimal varieties of PI-superalgebras with graded involution ⋮ Varieties of algebras with pseudoinvolution and polynomial growth ⋮ Algebras with involution and multiplicities bounded by a constant ⋮ Polynomial codimension growth of algebras with involutions and superinvolutions ⋮ Central polynomials with involution for the algebra of 2 × 2 upper triangular matrices ⋮ On PI-algebras with additional structures: rationality of Hilbert series and Specht's problem ⋮ Some results concerning the multiplicities of cocharacters of superalgebras with graded involution ⋮ Growth of central polynomials of algebras with involution ⋮ Asymptotics for Capelli polynomials with involution

Cites Work

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• Kemer's theorem for affine PI algebras over a field of characteristic zero.
• Kemer's theory for \(H\)-module algebras with application to the PI exponent
• Varieties of algebras with superinvolution of almost polynomial growth
• Wreath products and P.I. algebras
• Representability and Specht problem for \(G\)-graded algebras.
• Amitsur's conjecture for associative algebras with a generalized Hopf action.
• Finitely generated algebras with involution and their identities.
• Identities in rings with involutions
• Existence of identities in \(A \otimes B\)
• Cocharacters, Codimensions and Hilbert Series of the Polynomial Identities for 2 × 2 Matrices with Involution

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