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| Author | : Percy Alexander MacMahon |
| Publisher | : MIT Press (MA) |
| Total Pages | : 992 |
| Release | : 1986 |
| Genre | : Mathematics |
| ISBN | : |
Some of the fifty-six papers in Volume II relate to combinatorics, but most of them investigate quite distinct areas and reveal a different side of MacMahons mind and mathematical originality.
| Author | : Wolfgang Lück |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 624 |
| Release | : 2002-08-06 |
| Genre | : Mathematics |
| ISBN | : 9783540435662 |
In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.
| Author | : Percy Alexander MacMahon |
| Publisher | : |
| Total Pages | : 992 |
| Release | : 1978 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Roe Goodman |
| Publisher | : Cambridge University Press |
| Total Pages | : 708 |
| Release | : 2000-01-13 |
| Genre | : Mathematics |
| ISBN | : 9780521663489 |
More than half a century has passed since Weyl's 'The Classical Groups' gave a unified picture of invariant theory. This book presents an updated version of this theory together with many of the important recent developments. As a text for those new to the area, this book provides an introduction to the structure and finite-dimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. The more advanced reader will find an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. This book will also serve as a reference for the main results on tensor and polynomial invariants and the finite-dimensional representation theory of the classical groups. It will appeal to researchers in mathematics, statistics, physics and chemistry whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.
| Author | : S.D. Adhikari |
| Publisher | : Springer |
| Total Pages | : 285 |
| Release | : 2009-06-15 |
| Genre | : Mathematics |
| ISBN | : 9386279460 |
This collection of articles contains the proceedings of the two international conferences (on Number Theory and Cryptography) held at the Harish - Chandra Research Institute. In recent years the interest in number theory has increased due to its applications in areas like error-correcting codes and cryptography. These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. While some papers do contain new results, several of the papers are expository articles that mention open questions, which will be useful to young researchers.
| Author | : Harm Derksen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 272 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 3662049589 |
This book, the first volume of a subseries on "Invariant Theory and Algebraic Transformation Groups", provides a comprehensive and up-to-date overview of the algorithmic aspects of invariant theory. Numerous illustrative examples and a careful selection of proofs make the book accessible to non-specialists.
| Author | : Roe Goodman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 731 |
| Release | : 2009-07-30 |
| Genre | : Mathematics |
| ISBN | : 0387798528 |
Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants: (1) Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus; (2) Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux); (3) Self-contained chapters, appendices, comprehensive bibliography; (4) More than 350 exercises (most with detailed hints for solutions) further explore main concepts; (5) Serves as an excellent main text for a one-year course in Lie group theory; (6) Benefits physicists as well as mathematicians as a reference work.
| Author | : Shigeru Mukai |
| Publisher | : Cambridge University Press |
| Total Pages | : 528 |
| Release | : 2003-09-08 |
| Genre | : Mathematics |
| ISBN | : 9780521809061 |
Sample Text
| Author | : Nolan R. Wallach |
| Publisher | : Springer |
| Total Pages | : 199 |
| Release | : 2017-09-08 |
| Genre | : Mathematics |
| ISBN | : 3319659073 |
Geometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. This sophisticated topic is elegantly presented with enough background theory included to make the text accessible to advanced graduate students in mathematics and physics with diverse backgrounds in algebraic and differential geometry. Throughout the book, examples are emphasized. Exercises add to the reader’s understanding of the material; most are enhanced with hints. The exposition is divided into two parts. The first part, ‘Background Theory’, is organized as a reference for the rest of the book. It contains two chapters developing material in complex and real algebraic geometry and algebraic groups that are difficult to find in the literature. Chapter 1 emphasizes the relationship between the Zariski topology and the canonical Hausdorff topology of an algebraic variety over the complex numbers. Chapter 2 develops the interaction between Lie groups and algebraic groups. Part 2, ‘Geometric Invariant Theory’ consists of three chapters (3–5). Chapter 3 centers on the Hilbert–Mumford theorem and contains a complete development of the Kempf–Ness theorem and Vindberg’s theory. Chapter 4 studies the orbit structure of a reductive algebraic group on a projective variety emphasizing Kostant’s theory. The final chapter studies the extension of classical invariant theory to products of classical groups emphasizing recent applications of the theory to physics.
| Author | : Alexander H. W. Schmitt |
| Publisher | : European Mathematical Society |
| Total Pages | : 404 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9783037190654 |
The book starts with an introduction to Geometric Invariant Theory (GIT). The fundamental results of Hilbert and Mumford are exposed as well as more recent topics such as the instability flag, the finiteness of the number of quotients, and the variation of quotients. In the second part, GIT is applied to solve the classification problem of decorated principal bundles on a compact Riemann surface. The solution is a quasi-projective moduli scheme which parameterizes those objects that satisfy a semistability condition originating from gauge theory. The moduli space is equipped with a generalized Hitchin map. Via the universal Kobayashi-Hitchin correspondence, these moduli spaces are related to moduli spaces of solutions of certain vortex type equations. Potential applications include the study of representation spaces of the fundamental group of compact Riemann surfaces. The book concludes with a brief discussion of generalizations of these findings to higher dimensional base varieties, positive characteristic, and parabolic bundles. The text is fairly self-contained (e.g., the necessary background from the theory of principal bundles is included) and features numerous examples and exercises. It addresses students and researchers with a working knowledge of elementary algebraic geometry.
