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The invariant theory of matrices

This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of m\times m matrices with coeffic...

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Detalles Bibliográficos
Autores principales: Concini, Corrado De, Procesi, Claudio
Lenguaje:eng
Publicado: American Mathematical Society 2017
Materias:
Acceso en línea:http://cds.cern.ch/record/2303964
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author Concini, Corrado De
Procesi, Claudio
author_facet Concini, Corrado De
Procesi, Claudio
author_sort Concini, Corrado De
collection CERN
description This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of m\times m matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving the first fundamental theorem that describes a set of generators in the ring of invariants, and the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, self-contained way in the book.
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spelling cern-23039642021-04-21T18:54:21Zhttp://cds.cern.ch/record/2303964engConcini, Corrado DeProcesi, ClaudioThe invariant theory of matricesMathematical Physics and MathematicsThis book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of m\times m matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving the first fundamental theorem that describes a set of generators in the ring of invariants, and the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, self-contained way in the book.American Mathematical Societyoai:cds.cern.ch:23039642017
spellingShingle Mathematical Physics and Mathematics
Concini, Corrado De
Procesi, Claudio
The invariant theory of matrices
title The invariant theory of matrices
title_full The invariant theory of matrices
title_fullStr The invariant theory of matrices
title_full_unstemmed The invariant theory of matrices
title_short The invariant theory of matrices
title_sort invariant theory of matrices
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2303964
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