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OverviewThe 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. Full Product DetailsAuthor: Frank D. GrosshansPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Volume: 1673 Dimensions: Width: 15.50cm , Height: 0.80cm , Length: 23.50cm Weight: 0.520kg ISBN: 9783540636281ISBN 10: 3540636285 Pages: 152 Publication Date: 18 November 1997 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction . . . . . . . . . . . . . . . . . . . . . . Chapter One - Observable Subgroups 1. Stabilizer Subgroups . . . . . . . . . . . . . . . 2. Equivalent Conditions. . . . . . . . . . . . . . . 3. Observable Subgroups of Reductive Groups . . . . . 4. Finite Generation of kAEG/HUE. . . . . . . . . . . . Appendix: On Valuation Rings. . . . . . . . . 5. Maximal Unipotent Subgroups. . . . . . . . . . . . Bibliographical Note. . . . . . . . . . . . . . . . . . Chapter Two - The Transfer Principle 6. Induced Modules. . . . . . . . . . . . . . . . . . Appendix: Affine Quotients and induced modules 7. Induced Modules and Observable Subgroups . . . . . Appendix: On a Theorem of F. A. Bogomolov . . 8. Counter-examples . . . . . . . . . . . . . . . . . 9. The Transfer Principle . . . . . . . . . . . . . . 10. The Theorems of Roberts and Weitzenb'ck. . . . . . 11. Geometric Examples . . . . . . . . . . . . . . . . A. Multiplicity-free actions . . . . . . . . B. Affine Geometry . . . . . . . . . . . . . C. Invariants of the Orthogonal Group. . . . D. Euclidean Geometry. . . . . . . . . . . . E. Hilbert's Example. . . . . . . . . . . . Chapter Three - Invariants of Maximal Unipotent Subgroups 12. The Representations E( ) . . . . . . . . . . . . . 13. An Example: The General Linear Group . . . . . . . A. Straightening . . . . . . . . . . . . . . B. U - invariants. . . . . . . . . . . . . . C. Results of K. Pommerening . . . . . . . . 14. The Relationship between A and G AU. . . . . . . . 15. The Algebra grA. . . . . . . . . . . . . . . . . . 16. Finite Generation and U-invariants . . . . . . . . A. Algebras. . . . . . . . . . . . . . . . . B. Modules . . . . . . . . . . . . . . . . . 17. S-varieties. . . . . . . . . . . . . . . . . . . . 18. Flat Deformations and Normality. . . . . . . . . . Bibliographical Note. . . . . . . . . . . . . . . . . . Chapter Four - Complexity 19. Basic Principles . . . . . . . . . . . . . . . . . Appendix: On Quotient Spaces . . .. . . . . 20. Unique Factorization Domains . . . . . . . . . . . A. c(X) = 0. . . . . . . . . . . . . . . . . B. c(X) = 1. . . . . . . . . . . . . . . . . 21. Complexity and Finite Generation . . . . . . . . . A. Statement of Results. . . . . . . . . . . B. Proof of Theorem 21.1 . . . . . . . . . . 22. Spherical Subgroups. . . . . . . . . . . . . . . . 23. Finite Generation of Induced Modules . . . . . . . A. Condition (FM). . . . . . . . . . . . . . B. Epimorphic Subgroups. . . . . . . . . . . Bibliographical Note. . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . List of Symbols. . . . . . . . . . . . . . . . . . . . . . Index. . . . . . . . . . . . . . . . . . . . . . . . . . .ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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