*-Polynomial Identities of Matrices with the Symplectic Involution: The Low Degrees

DOI10.1081/AGB-120027957zbMath1068.16029OpenAlexW2047016980MaRDI QIDQ3154499

Michel L. Racine, Alain D'Amour

Publication date: 14 January 2005

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

Full work available at URL: https://doi.org/10.1081/agb-120027957

zbMATH Keywords

*-polynomial identitiessymplectic involutionsmatrix algebras with involution

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 (7)

Minimal degree of identities of matrix algebras with additional structures ⋮ An identity of degree \(2n - 3\) for the \(n{\times}n\) skews, \(n\) even, and corollaries for standard identities ⋮ Polynomial identities for matrices symmetric with respect to the symplectic involution. ⋮ Matrix identities involving multiplication and transposition. ⋮ Jordan triple systems of degree at most 2 ⋮ Identities with involution for the matrix algebra of order two in characteristic \(p\). ⋮ Matrix algebras with involution and standard polynomial identities in symmetric variables

Cites Work

• A Lie algebra generalization of the Amitsur-Levitski theorem
• Central polynomials for Jordan algebras. I
• Finite basing of the identities of a matrix algebra of second order over a field of characteristic zero
• On *-polynomial identities for n\(\times n\) matrices
• Identities in rings with involutions
• Minimal Identities of Symmetric Matrices
• Minimal identities for jordan algebras of degree 2
• A simple proof of Kostant’s theorem, and an analogue for the symplectic involution
• *-polynomial identities of matrices with the transpose involution: The low degrees
• Cocharacters, Codimensions and Hilbert Series of the Polynomial Identities for 2 × 2 Matrices with Involution

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