Defining relations for the algebra of invariants of \(2\times 2\) matrices
type: Item
instance of: scholarly article
title: Defining relations for the algebra of invariants of \(2\times 2\) matrices
zbMATH Open document ID: 1026.16009
DOI: 10.1023/A:1023266314025
author: Vesselin Drensky
published in: Algebras and Representation Theory
publication date: 2003-06-09T00:00:00Z
review text: Let \(G\) be a subgroup of the general linear group \(\text{GL}_2\) over the complex numbers, and assume that \(G\) acts by conjugation on the \(m\)-tuples of \(2\times 2\) matrices. The invariants of such actions are of significant importance in the study of the polynomial identities satisfied by algebras related to \(M_2\). The paper under review describes the defining relations of the algebras of invariants of this action when \(G\) is either \(\text{GL}_2\), or \(\text{O}_2\), the orthogonal group, or \(\text{SO}_2\), the special orthogonal group. The main techniques used in the proofs of these results are derived from the classical invariant theory as well as from the representation theory of the general linear group. The results of the paper will be of interest for the specialists in invariant theory, and especially for those involved in PI theory.
Mathematics Subject Classification ID: 16R30
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 1925057
zbMATH Keywords: defining relations of matrix invariants
zbMATH Keywords: generic matrices
zbMATH Keywords: actions of general linear groups
reviewed by: Plamen Koshlukov
MaRDI profile type: Publication
full work available at URL: a:1023266314025
OpenAlex ID: W139468346
description: scientific article; zbMATH DE number 1925057