A simple proof of Kostant’s theorem, and an analogue for the symplectic involution

DOI10.1090/conm/013/685953zbMath0503.16018OpenAlexW4238834498MaRDI QIDQ3969084

Louis Halle Rowen

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1090/conm/013/685953

zbMATH Keywords

matrix algebrageneric polynomialtrace identitytransposesymplectic involutionstandard identityAmitsur-Levitzki theoremskew- symmetric elements

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Finite rings and finite-dimensional associative algebras (16P10) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Rings with polynomial identity (16Rxx)

Related Items (17)

*-Polynomial Identities of Matrices with the Symplectic Involution: The Low Degrees ⋮ Minimal degree of identities of matrix algebras with additional structures ⋮ Standard polynomials and matrices with superinvolutions ⋮ *-polynomial identities of matrices with the transpose involution: The low degrees ⋮ An identity of degree \(2n - 3\) for the \(n{\times}n\) skews, \(n\) even, and corollaries for standard identities ⋮ Identities of symmetric and skew-symmetric matrices in characteristic \(p\) ⋮ Minimal degree of standard identities of matrix algebras with symplectic graded involution ⋮ On the minimal degree of the \(*\)-polynomial identities for the matrix algebra of order \(6\) with symplectic involution ⋮ On certain modules of covariants in exterior algebras ⋮ Invariant theory in exterior algebras and Amitsur-Levitzki type theorems ⋮ Polynomial identities for matrices symmetric with respect to the symplectic involution. ⋮ On minimal ∗-identities of matrices^∗ ⋮ Standard identities for skew-symmetric matrices ⋮ Associative rings ⋮ On *-polynomial identities for n\(\times n\) matrices ⋮ Trace Identities for Matrices with the Transpose Involution ⋮ Matrix algebras with involution and standard polynomial identities in symmetric variables

This page was built for publication: A simple proof of Kostant’s theorem, and an analogue for the symplectic involution