書誌事項

The invariant theory of matrices

Corrado De Concini, Claudio Procesi

(University lecture series, v. 69)

American Mathematical Society, c2017

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注記

Includes bibliographical references (p. 145-148) and indexes

内容説明・目次

内容説明

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.

目次

Introduction 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.

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詳細情報

  • NII書誌ID(NCID)
    BB24965840
  • ISBN
    • 9781470441876
  • LCCN
    2017041943
  • 出版国コード
    us
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Providence, R.I.
  • ページ数/冊数
    v, 151 p.
  • 大きさ
    26 cm
  • 分類
  • 件名
  • 親書誌ID
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