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OverviewThis 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. Full Product DetailsAuthor: Corrado De Concini , Claudio ProcesiPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.295kg ISBN: 9781470441876ISBN 10: 147044187 Pages: 153 Publication Date: 30 December 2017 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction and preliminaries The classical theory Quasi-hereditary algebras The Schur algebra Matrix functions and invariants Relations The Schur algebra of a free algebra Bibliography General index Symbol index.ReviewsThe present book is a nice and introductory reference to graduate students or researchers who are working in the field of representation and invariant theory. - Yin Chen, Zentralblatt MATH The choices made by the authors permit them to highlight the main results and also to keep the material within the reach of an interested reader. At the same time, the book remains open-ended with precise pointers to the literature on other approaches and the cases not treated here. - Felipe Zaldivar, MAA Reviews "The present book is a nice and introductory reference to graduate students or researchers who are working in the field of representation and invariant theory."" — Yin Chen, Zentralblatt MATH ""The choices made by the authors permit them to highlight the main results and also to keep the material within the reach of an interested reader. At the same time, the book remains open-ended with precise pointers to the literature on other approaches and the cases not treated here."" — Felipe Zaldivar, MAA Reviews" Author InformationCorrado De Concini, Sapienza Universita di Roma, Rome, Italy. Claudio Procesi, Sapienza Universita di Roma, Rome, Italy. Tab Content 6Author Website:Countries AvailableAll regions |
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