Overview

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.

Full Product Details

Author:   H.E.A. Eddy Campbell ,  David L. Wehlau
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2011 ed.
Volume:   139
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   0.541kg
ISBN:  

9783642174032

ISBN 10:   3642174035
Pages:   234
Publication Date:   14 January 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 First Steps.- 2 Elements of Algebraic Geometry and Commutative Algebra.- 3 Applications of Commutative Algebra to Invariant Theory.- 4 Examples.- 5 Monomial Orderings and SAGBI Bases.- 6 Block Bases.- 7 The Cyclic Group Cp.- 8 Polynomial Invariant Rings.- 9 The Transfer.- 10 Invariant Rings via Localization.- 11 Rings of Invariants which are Hypersurfaces.- 12 Separating Invariants.- 13 Using SAGBI Bases to Compute Rings of Invariants.- 14 Ladders.- References.- Index.

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)"

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)

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)

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