Modular Invariant Theory

1. Front Matter

   Pages I-XIII

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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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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.

• Finite groups
• Modular invariant theory

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)

• 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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