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Modular Invariant Theory

  • Book
  • © 2011

Overview

Authors:
  1. H.E.A. Eddy Campbell

    1. Sir Howard Douglas Hall, Dept. Mathematics, University of New Brunswick, Fredericton, Canada

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    You can also search for this author in PubMed   Google Scholar

  2. David L. Wehlau

    1. Dept. Mathematics & Computer Science, Royal Military College of Canada, Kingston, Canada

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Illustration of techniques and phenomena
  • Can be used as a graduate textbook
  • Includes supplementary material: sn.pub/extras

Part of the book series: Encyclopaedia of Mathematical Sciences (EMS, volume 139)

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Table of contents (14 chapters)

  1. Front Matter

    Pages I-XIII
    Download chapter PDF

  2. First Steps

    • H. E. A. Eddy Campbell, David L. Wehlau
    Pages 1-24

  3. Elements of Algebraic Geometry and Commutative Algebra

    • H. E. A. Eddy Campbell, David L. Wehlau
    Pages 25-37

  4. Applications of Commutative Algebra to Invariant Theory

    • H. E. A. Eddy Campbell, David L. Wehlau
    Pages 39-57

  5. Examples

    • H. E. A. Eddy Campbell, David L. Wehlau
    Pages 59-81

  6. Monomial Orderings and SAGBI Bases

    • H. E. A. Eddy Campbell, David L. Wehlau
    Pages 83-97

  7. Block Bases

    • H. E. A. Eddy Campbell, David L. Wehlau
    Pages 99-104

  8. The Cyclic Group C p

    • H. E. A. Eddy Campbell, David L. Wehlau
    Pages 105-139

  9. Polynomial Invariant Rings

    • H. E. A. Eddy Campbell, David L. Wehlau
    Pages 141-151

  10. The Transfer

    • H. E. A. Eddy Campbell, David L. Wehlau
    Pages 153-177

  11. Invariant Rings via Localization

    • H. E. A. Eddy Campbell, David L. Wehlau
    Pages 179-184

  12. Rings of Invariants which are Hypersurfaces

    • H. E. A. Eddy Campbell, David L. Wehlau
    Pages 185-189

  13. Separating Invariants

    • H. E. A. Eddy Campbell, David L. Wehlau
    Pages 191-203

  14. Using SAGBI Bases to Compute Rings of Invariants

    • H. E. A. Eddy Campbell, David L. Wehlau
    Pages 205-210

  15. Ladders

    • H. E. A. Eddy Campbell, David L. Wehlau
    Pages 211-221

  16. Back Matter

    Pages 223-233
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Keywords

About this book

This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the better understood non-modular setting. It details techniques for the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of many topics as well as a quick survey of the elements of algebraic geometry and commutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchers—an introduction to many important topics in modern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter.

Reviews

From the reviews:

“Modular Invariant Theory is a fitting entry into the ‘Encyclopaedia of mathematical Sciences’ series: it deals with important living mathematics in a way suited to researchers both at the rookie and more advanced levels.” (Michael Berg, The Mathematical Association of America, March, 2011)

“Provide the necessary background in commutative algebra, algebraic geometry, monomial orderings, and SAGBI bases and give many examples. The book should be accessible to second or third year graduate students and will bring any reader up to date on an active area of research.” (Frank D. Grosshans, Mathematical Reviews, Issue 2012 b)

“The book is a good source for examples and inspirations in modular invariant theory. … it is well suited for researchers who aim to get a feeling for recent problems in modular invariant theory and related problems. It can also be used as a companion book for a graduate course in invariant theory of finite groups with a view towards the differences to the modular case.” (Peter Schenzel, Zentralblatt MATH, Vol. 1216, 2011)

Authors and Affiliations

  • Sir Howard Douglas Hall, Dept. Mathematics, University of New Brunswick, Fredericton, Canada

    H.E.A. Eddy Campbell

  • Dept. Mathematics & Computer Science, Royal Military College of Canada, Kingston, Canada

    David L. Wehlau

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