Polynomial identities for matrices symmetric with respect to the symplectic involution.

DOI10.1016/J.JALGEBRA.2011.10.023zbMath1251.16019OpenAlexW2033554998MaRDI QIDQ420664

Jordan Dale Hill

Publication date: 23 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2011.10.023

zbMATH Keywords

symmetric matricespolynomial identitiessymplectic involution\(*\)-identitiesstandard identity

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 (6)

Minimal degree of identities of matrix algebras with additional structures ⋮ Standard polynomials and matrices with superinvolutions ⋮ An identity of degree \(2n - 3\) for the \(n{\times}n\) skews, \(n\) even, and corollaries for standard identities ⋮ Lie properties in associative algebras ⋮ A study of inverse problems based on two kinds of special matrix equations in Euclidean space ⋮ Matrix algebras with involution and standard polynomial identities in symmetric variables

Cites Work

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• Standard identities for skew-symmetric matrices
• The invariant theory of \(n\times n\) matrices
• \(*\)-identities of minimal degree in matrix algebras of low order
• Identities in rings with involutions
• *-Polynomial Identities of Matrices with the Symplectic Involution: The Low Degrees
• Minimal identities for jordan algebras of degree 2
• A simple proof of Kostant’s theorem, and an analogue for the symplectic involution
• TRACE IDENTITIES OF FULL MATRIX ALGEBRAS OVER A FIELD OF CHARACTERISTIC ZERO
• Minimal Identities for Algebras

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