Involution codimensions of finite dimensional algebras and exponential growth

DOI10.1006/jabr.1999.8016zbMath0944.16023OpenAlexW2090000503MaRDI QIDQ1969365

Antonio Giambruno, Mikhail V. Zaicev

Publication date: 27 June 2000

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

Full work available at URL: https://doi.org/10.1006/jabr.1999.8016

zbMATH Keywords

codimension sequences\(*\)-polynomial identitiescodimensions of \(T\)-idealsfinite dimensional algebras with involutions

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) 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 (24)

ALGEBRAS WITH INVOLUTION WHOSE EXPONENT OF THE *-CODIMENSIONS IS EQUAL TO TWO ⋮ On the asymptotics of Capelli polynomials ⋮ Trace identities on diagonal matrix algebras ⋮ On codimensions of algebras with involution ⋮ On the *-Polynomial Identities of a Class of *-Minimal Algebras ⋮ Star-polynomial identities: computing the exponential growth of the codimensions ⋮ The exponent for superalgebras with superinvolution ⋮ *-Graded Capelli polynomials and their asymptotics ⋮ Codimensions of algebras with additional structures ⋮ Comparing the \(\mathbb{Z}_2\)-graded identities of two minimal superalgebras with the same superexponent ⋮ Polynomial identities on superalgebras and exponential growth ⋮ Star-fundamental algebras: polynomial identities and asymptotics ⋮ Classifying \(G\)-graded algebras of exponent two ⋮ Exponents of identities of group rings. ⋮ Some characterizations of algebras with involution with polynomial growth of their codimensions ⋮ \(\ast\)-Superalgebras and exponential growth ⋮ Minimal algebras with respect to their *-exponent. ⋮ A characterization of *-minimal algebras with involution. ⋮ \(*\)-polynomial identities of a nonsymmetric \(*\)-minimal algebra. ⋮ On the *-minimality of algebras with involution. ⋮ A characterization of superalgebras with pseudoinvolution of exponent 2 ⋮ Polynomial growth and identities of superalgebras and star-algebras. ⋮ Understanding star-fundamental algebras ⋮ Asymptotics for Capelli polynomials with involution

Cites Work

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• Homology of symplectic and orthogonal algebras
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• Exponential codimension growth of PI algebras: an exact estimate
• Asymptotic values for degrees associated with strips of Young diagrams
• Identities in rings with involutions
• $G$-identities on associative algebras
• Cocharacters, Codimensions and Hilbert Series of the Polynomial Identities for 2 × 2 Matrices with Involution
• A characterization of algebras with polynomial growth of the codimensions

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