Algorithms in Invariant Theory

✍ Scribed by Dr. Bernd Sturmfels (auth.)

• Publisher: Springer-Verlag Wien
• Year: 2008
• Tongue: English
• Leaves: 201
• Series: Texts and Monographs in Symbolic Computation
• Edition: 2
• Category: Library

✦ Synopsis

J. Kung and G.-C. Rota, in their 1984 paper, write: “Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics”. The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students will find the book an easy introduction to this “classical and new” area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to a wealth of research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems.

✦ Table of Contents

Front Matter....Pages I-VII
Introduction....Pages 1-23
Invariant theory of finite groups....Pages 25-75
Bracket algebra and projective geometry....Pages 77-135
Invariants of the general linear group....Pages 137-190
Back Matter....Pages 191-197

✦ Subjects

Mathematical Logic and Formal Languages; Combinatorics; Artificial Intelligence (incl. Robotics); Symbolic and Algebraic Manipulation; Mathematical Logic and Foundations; Algebraic Geometry