Invariant Theory of Finite Groups

  • David A. Cox
  • John Little
  • Donal O’Shea
Chapter
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Invariant theory has had a profound effect on the development of algebraic geometry. For example, the Hilbert Basis Theorem and Hilbert Nullstellensatz, which play a central role in the earlier chapters in this book, were proved by Hilbert in the course of his investigations of invariant theory.In this chapter, we will study the invariants of finite groups. The basic goal is to describe all polynomials that are unchanged when we change variables according to a given finite group of matrices. Our treatment will be elementary and by no means complete. In particular, we do not presume a prior knowledge of group theory.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • David A. Cox
    • 1
  • John Little
    • 2
  • Donal O’Shea
    • 3
  1. 1.Department of MathematicsAmherst CollegeAmherstUSA
  2. 2.Department of Mathematics and Computer ScienceCollege of the Holy CrossWorcesterUSA
  3. 3.President’s OfficeNew College of FloridaSarasotaUSA

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