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Reflection Groups And Coxeter Groups

Reflection Groups and Coxeter Groups PDF
Author: James E. Humphreys
Publisher: Cambridge University Press
ISBN: 9780521436137
Size: 21.85 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 204
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A self-contained graduate textbook introducing the basic theory of Coxeter groups.

Reflection Groups And Invariant Theory

Reflection Groups and Invariant Theory PDF
Author: Richard Kane
Publisher: Springer Science & Business Media
ISBN: 1475735421
Size: 36.97 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 379
View: 458

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Reflection groups and invariant theory is a branch of mathematics that lies at the intersection between geometry and algebra. The book contains a deep and elegant theory, evolved from various graduate courses given by the author over the past 10 years.

Reflection Groups And Invariant Theory

Reflection Groups and Invariant Theory PDF
Author: Richard Kane
Publisher: Springer Science & Business Media
ISBN: 9780387989792
Size: 29.87 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 379
View: 3184

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Reflection groups and invariant theory is a branch of mathematics that lies at the intersection between geometry and algebra. The book contains a deep and elegant theory, evolved from various graduate courses given by the author over the past 10 years.

Groups Of Exceptional Type Coxeter Groups And Related Geometries

Groups of Exceptional Type  Coxeter Groups and Related Geometries PDF
Author: N.S. Narasimha Sastry
Publisher: Springer Science & Business Media
ISBN: 8132218140
Size: 63.92 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 304
View: 2679

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The book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the theme of the book. Some of the articles provide the latest developments in the subject; some provide an overview of the current status of some important problems in this area; some survey an area highlighting the current developments; and some provide an exposition of an area to collect problems and conjectures. It is hoped that these articles would be helpful to a beginner to start independent research on any of these topics, as well as to an expert to know some of the latest developments or to consider some problems for investigation.

The Geometry And Topology Of Coxeter Groups Lms 32

The Geometry and Topology of Coxeter Groups   LMS 32  PDF
Author: Michael Davis
Publisher: Princeton University Press
ISBN: 1400845947
Size: 16.41 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 600
View: 4671

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The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.

Coxeter Matroids

Coxeter Matroids PDF
Author: Alexandre V. Borovik
Publisher: Springer Science & Business Media
ISBN: 1461220661
Size: 60.56 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 266
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Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry, and "Coxeter Matroids" provides an intuitive and interdisciplinary treatment of their theory. In this text, matroids are examined in terms of symmetric and finite reflection groups; also, symplectic matroids and the more general coxeter matroids are carefully developed. The Gelfand-Serganova theorem, which allows for the geometric interpretation of matroids as convex polytopes with certain symmetry properties, is presented, and in the final chapter, matroid representations and combinatorial flag varieties are discussed. With its excellent bibliography and index and ample references to current research, this work will be useful for graduate students and research mathematicians.

Finite Reflection Groups

Finite Reflection Groups PDF
Author: L.C. Grove
Publisher: Springer Science & Business Media
ISBN: 1475718691
Size: 21.12 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 136
View: 2540

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Chapter 1 introduces some of the terminology and notation used later and indicates prerequisites. Chapter 2 gives a reasonably thorough account of all finite subgroups of the orthogonal groups in two and three dimensions. The presentation is somewhat less formal than in succeeding chapters. For instance, the existence of the icosahedron is accepted as an empirical fact, and no formal proof of existence is included. Throughout most of Chapter 2 we do not distinguish between groups that are "geo metrically indistinguishable," that is, conjugate in the orthogonal group. Very little of the material in Chapter 2 is actually required for the sub sequent chapters, but it serves two important purposes: It aids in the development of geometrical insight, and it serves as a source of illustrative examples. There is a discussion offundamental regions in Chapter 3. Chapter 4 provides a correspondence between fundamental reflections and funda mental regions via a discussion of root systems. The actual classification and construction of finite reflection groups takes place in Chapter 5. where we have in part followed the methods of E. Witt and B. L. van der Waerden. Generators and relations for finite reflection groups are discussed in Chapter 6. There are historical remarks and suggestions for further reading in a Post lude.

The Coxeter Legacy

The Coxeter Legacy PDF
Author: Harold Scott Macdonald Coxeter
Publisher: American Mathematical Soc.
ISBN: 9780821887608
Size: 79.63 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 320
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This collection of essays on the legacy of mathematican Donald Coxeter is a mixture of surveys, updates, history, storytelling and personal memories covering both applied and abstract maths. Subjects include: polytopes, Coxeter groups, equivelar polyhedra, Ceva's theorum, and Coxeter and the artists.

Geometric Combinatorics

Geometric Combinatorics PDF
Author: Ezra Miller
Publisher: American Mathematical Soc.
ISBN: 9780821886953
Size: 60.50 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 691
View: 172

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Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.

Lattice Theory Special Topics And Applications

Lattice Theory  Special Topics and Applications PDF
Author: George Grätzer
Publisher: Birkhäuser
ISBN: 3319442368
Size: 42.63 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 616
View: 196

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George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, in two volumes, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This second volume is divided into ten chapters contributed by K. Adaricheva, N. Caspard, R. Freese, P. Jipsen, J.B. Nation, N. Reading, H. Rose, L. Santocanale, and F. Wehrung.