The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years. This book is an exposition of several related topics including observable subgroups, induced modules, maximal unipotent subgroups of reductive groups and the method of U-invariants, and the complexity of an action. Much of this material has not appeared previously in book form. The exposition assumes a basic knowledge of algebraic groups and then develops each topic systematically with applications to invariant theory. Exercises are included as well as many examples, some of which are related to geometry and physics.

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Bibliographic Information

Book Title: Algebraic Homogeneous Spaces and Invariant Theory
Authors: Frank D. Grosshans
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0093525
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1997
Softcover ISBN: 978-3-540-63628-1Published: 18 November 1997
eBook ISBN: 978-3-540-69617-9Published: 14 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 152
Topics: Group Theory and Generalizations, Algebraic Geometry, Linear and Multilinear Algebras, Matrix Theory

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Table of contents (6 chapters)

Front Matter

Introduction

Observable subgroups

The transfer principle

Invariants of maximal unipotent subgroups

Complexity

Erratum

Back Matter

About this book