Multiplicative Invariant Theory

1. Auflage 2005
ISBN: 978-3-540-24323-6
Verlag: Springer-Verlag GmbH

Buch, Englisch, Band 135, 180 Seiten, Format (B × H): 162 mm x 241 mm, Gewicht: 398 g

Reihe: Encyclopaedia of Mathematical Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Lorenz, Martin

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

Notations and Conventions.- Groups Acting on Lattices.- Permutation Lattices and Flasque Equivalence.- Multiplicative Actions.- Class Group.- Picard Group.- Multiplicative Invariants of Reflection Groups.- Regularity.- The Cohen-Macaulay Property.- Multiplicative Invariant Fields.- Problems.