Computational Invariant TheorySpringer Science & Business Media, 17 avr. 2013 - 268 pages Invariant theory is a subject with a long tradition and an astounding abil ity to rejuvenate itself whenever it reappears on the mathematical stage. Throughout the history of invariant theory, two features of it have always been at the center of attention: computation and applications. This book is about the computational aspects of invariant theory. We present algorithms for calculating the invariant ring of a group that is linearly reductive or fi nite, including the modular case. These algorithms form the central pillars around which the book is built. To prepare the ground for the algorithms, we present Grabner basis methods and some general theory of invariants. Moreover, the algorithms and their behavior depend heavily on structural properties of the invariant ring to be computed. Large parts of the book are devoted to studying such properties. Finally, most of the applications of in variant theory depend on the ability to calculate invariant rings. The last chapter of this book provides a sample of applications inside and outside of mathematics. |
Table des matières
| 1 | |
Invariant Theory 39 | 33 |
Invariant Theory of Finite Groups | 73 |
Invariant Theory of Reductive Groups | 139 |
Applications of Invariant Theory 209 | 208 |
A Linear Algebraic Groups | 237 |
References | 247 |
| 261 | |
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Expressions et termes fréquents
A-module affine variety algorithm assume binary forms calculated char(K characteristic coefficients compute coordinate ring Corollary defined degree bound dimension elementary symmetric polynomials elements Equation Example exists field finite dimensional finite groups follows G acts G-stable G-variety geometric given GL(V graded algebra Gröbner basis group G Hence Hilbert series homogeneous invariants homogeneous system homomorphism ideal integral invariant ring K[V]G invariant theory invariants of degree irreducible isomorphic Kemper kernel KG-module Lemma Let G linear algebraic group linearly reductive group Math matrix maximal minimal modular module Molien's formula monomial ordering morphism multiple Noether non-zero normal form obtain orbit permutation polynomial ring Popov primary invariants Proof Proposition quotient rational representation Red(t reductive group reflection group representation of G Reynolds operator secondary invariants Section subalgebra subgroup subset symmetric symmetric group system of parameters Theorem torus vector space Zariski zero