The polynomial identities of matrices

DOI10.1090/conm/013/685937zbMath0503.16016OpenAlexW4251619236MaRDI QIDQ3969082

Edward W. Formanek

Publication date: 1982

Published in: Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/013/685937

zbMATH Keywords

surveyirreducible representationsT-idealstrace identitiespolynomial identities of matricestracescyclic algebrasYoung diagramsBrauer groupcodimensionscentral polynomialsPI-ringscocharactersweak identitiestensor product theoremAmitsur-Levitzki theoremCapelli polynomialsring of generic matricesgeneric division ringlinearization of identitiesrepresentation theory of the symmetric and general linear groups

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Endomorphism rings; matrix rings (16S50) Representations of finite symmetric groups (20C30) Research exposition (monographs, survey articles) pertaining to associative rings and algebras (16-02) Rings with polynomial identity (16Rxx)

Related Items (17)

Some Consequences of the Standard Polynomial ⋮ Alcuni metodi computazionali in algebra ⋮ New automorphisms of generic matrix algebras and polynomial algebras ⋮ \(H^3\) and generic matrices ⋮ Some remarks on rational matrix invariants ⋮ Explicit codimension formulas of certain T-ideals ⋮ A new central polynomial for 3 × 3 matrices ⋮ Inequalities for numerical invariants of sets of matrices ⋮ Computable identities in the algebra of formal matrices ⋮ Associative rings ⋮ A conjecture of Regev about the Capelli polynomial ⋮ Polynomial identities for 2\(\times 2\) matrices ⋮ Rational function fields. Noether's problem and related questions ⋮ Codimensions and trace codimensions of matrices are asymptotically equal ⋮ Invariants and the ring of generic matrices ⋮ On a question concerning generic matrices over the integers ⋮ The Brauer group and the center of generic matrices

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