Glxgl- representations and ∗-polynomial identities

DOI10.1080/00927878608823335zbMath0604.16018OpenAlexW2095921825MaRDI QIDQ3741754

Antonio Giambruno

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1080/00927878608823335

zbMATH Keywords

algebras with involutionsymmetric groupT-idealspolynomial identitiesYoung diagramswreath productrelatively free algebrastensor powercocharactersrepresentations of general linear groupsmultihomogeneous identitiesmultilinear tensors

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Representations of finite symmetric groups (20C30) Representation theory for linear algebraic groups (20G05) Vector and tensor algebra, theory of invariants (15A72) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Rings with polynomial identity (16Rxx)

Related Items (23)

On the *-Polynomial Identities of a Class of *-Minimal Algebras ⋮ Cocharacters of \(\mathbb Z/2\mathbb Z\)-graded algebras ⋮ Algebras with involution with linear codimension growth. ⋮ Identities and cocharacters of the algebra of \(3 \times 3\) matrices with non-trivial grading and transpose graded involution ⋮ On \(*\)-cocharacters of \(M_{1,1}(E)\). ⋮ On unitary algebras with graded involution of quadratic growth ⋮ Supervarieties of small graded colength. ⋮ Minimal star-varieties of polynomial growth and bounded colength ⋮ On minimal ∗-identities of matrices^∗ ⋮ Rappresentazioni di gruppi simmetrici ed identita' polinomiali ⋮ Graded cocharacters of minimal subvarieties of supervarieties of almost polynomial growth. ⋮ Colength of \(\ast\)-polynomial identities of simple \(\ast\)-algebras ⋮ Involution codimensions and trace codimensions of matrices are asymptotically equal ⋮ \(*\)-polynomial identities of a nonsymmetric \(*\)-minimal algebra. ⋮ Superalgebras with graded involution: classifying minimal varieties of quadratic growth ⋮ Super-cocharacters, star-cocharacters and multiplicities bounded by one. ⋮ Denominators for the Poincaré series of invariants of matrices with involution. ⋮ Minimal \(\ast\)-varieties and minimal supervarieties of polynomial growth ⋮ Matrices with involution and invariant theory ⋮ On the graded identities and cocharacters of the algebra of \(3\times 3\) matrices ⋮ Superalgebras with graded involution and star-graded colength bounded by 3 ⋮ On the \(*\)-cocharacter sequence of \(3\times 3\) matrices ⋮ Superalgebras and algebras with involution: classifying varieties of quadratic growth

Cites Work

• Homogeneous polynomial identities
• Wreath products and P.I. algebras
• Unnamed Item

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