Multiplicative Invariant Theory

  • Martin┬áLorenz

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 135)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Pages 1-7
  3. Pages 69-75
  4. Pages 77-84
  5. Pages 95-101
  6. Pages 149-160
  7. Back Matter
    Pages 161-177

About this book


Multiplicative invariant theory, as a research area in its own right within the wider spectrum of invariant theory, is of relatively recent vintage. The present text offers a coherent account of the basic results achieved thus far..

Multiplicative invariant theory is intimately tied to integral representations of finite groups. Therefore, the field has a predominantly discrete, algebraic flavor. Geometry, specifically the theory of algebraic groups, enters through Weyl groups and their root lattices as well as via character lattices of algebraic tori.

Throughout the text, numerous explicit examples of multiplicative invariant algebras and fields are presented, including the complete list of all multiplicative invariant algebras for lattices of rank 2.

The book is intended for graduate and postgraduate students as well as researchers in integral representation theory, commutative algebra and, mostly, invariant theory.


Algebra Permutation commutative rings field theory integral representation theory of finite groups invariant theory transformation groups

Authors and affiliations

  • Martin┬áLorenz
    • 1
  1. 1.Department of MathematicsTemple UniversityPhiladelphiaUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2005
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-24323-6
  • Online ISBN 978-3-540-27358-5
  • Series Print ISSN 0938-0396
  • Buy this book on publisher's site