A functional interpretation of the ring of matrix invariants
type: Item
instance of: scholarly article
title: A functional interpretation of the ring of matrix invariants
zbMATH Open document ID: 0714.16017
DOI: 10.1016/0021-8693(91)90055-D
author: Zinovy Reichstein
published in: Journal of Algebra
publication date: 1991-01-01T00:00:00Z
review text: Let k be an algebraically closed field of characteristic zero and \(C=C(n,m)\) be the ring of invariants of m-tuples of \(n\times n\) matrices over k. Some properties of the quotient space \(Q=Spec C\) are found in the paper. The main result (Theorem 3.3) states that if R is a commutative k- algebra and G(R) is the set of all irreducible representations of \(R\otimes L\) (L is the free associative algebra of rank m) in universal Cayley-Hamilton algebras then the functor G is represented by Q. Some sufficient conditions for a universal Cayley-Hamilton algebra having a unique trace function are given in the paper. A classification of universal Cayley-Hamilton algebras over an algebraically closed field is obtained.
reviewed by: Plamen Koshlukov
Mathematics Subject Classification ID: 16R30
Mathematics Subject Classification ID: 16R20
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 4175185
zbMATH Keywords: matrix invariants
zbMATH Keywords: trace rings
zbMATH Keywords: ring of invariants
zbMATH Keywords: irreducible representations
zbMATH Keywords: universal Cayley-Hamilton algebras
zbMATH Keywords: trace function
MaRDI profile type: Publication
Wikidata QID: Q117378985
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description: scientific article; zbMATH DE number 4175185