Classical Invariant Theory

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Cambridge University Press, 13.01.1999 - 280 Seiten
There has been a resurgence of interest in classical invariant theory driven by several factors: new theoretical developments; a revival of computational methods coupled with powerful new computer algebra packages; and a wealth of new applications, ranging from number theory to geometry, physics to computer vision. This book provides readers with a self-contained introduction to the classical theory as well as modern developments and applications. The text concentrates on the study of binary forms (polynomials) in characteristic zero, and uses analytical as well as algebraic tools to study and classify invariants, symmetry, equivalence and canonical forms. A variety of innovations make this text of interest even to veterans of the subject; these include the use of differential operators and the transform approach to the symbolic method, extension of results to arbitrary functions, graphical methods for computing identities and Hilbert bases, complete systems of rationally and functionally independent covariants, introduction of Lie group and Lie algebra methods, as well as a new geometrical theory of moving frames and applications. Aimed at advanced undergraduate and graduate students the book includes many exercises and historical details, complete proofs of the fundamental theorems, and a lively and provocative exposition.
 

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Inhalt

Prelude Quadratic Polynomials
1
Basic Invariant Theory for Binary Forms
11
Groups and Transformations
44
Representations and Invariants
62
Transvectants
86
Symbolic Methods
100
Graphical Methods
128
Gordans Method
143
Lie Groups and Moving Frames
150
Infinitesimal Methods
198
References
247
Author Index
260
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