Identities of representations of Lie algebras and *-polynomial identities
type: Item
instance of: scholarly article
title: Identities of representations of Lie algebras and *-polynomial identities
zbMATH Open document ID: 0919.16019
DOI: 10.1007/BF02844386
publication date: 1999-05-26T00:00:00Z
review text: The authors study *-polynomial identities of the \(2n\times 2n\) matrix algebra \(M_{2n}(K,^*)\) with symplectic involution. The main result is a criterion for a *-polynomial in skew-symmetric variables of a special kind to be an identity. This result is also restated for weak identities of the natural \(2n\)-dimensional representation of the symplectic Lie algebra.
Mathematics Subject Classification ID: 16R10
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 16R50
Mathematics Subject Classification ID: 16W10
zbMATH DE Number: 1279158
zbMATH Keywords: *-polynomial identities
zbMATH Keywords: algebras with involutions
zbMATH Keywords: weak identities
author: Tsetska Rashkova
author: Vesselin Drensky
reviewed by: Victor Petrogradsky
MaRDI profile type: Publication
cites work: Q4095018
cites work: Gröbner bases of certain determinantal ideals
cites work: Weak polynomial identities for the matrix algebras
cites work: Central polynomials for matrix rings
cites work: On minimal ∗-identities of matrices∗
cites work: Central and weak identities for matrices
full work available at URL: https://doi.org/10.1007/bf02844386
OpenAlex ID: W1995289368
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 1279158