The Geometry Of The Classical Groups
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The Geometry Of The Classical Groups
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Author : Donald E. Taylor
language : en
Publisher:
Release Date : 1992
The Geometry Of The Classical Groups written by Donald E. Taylor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
Groups And Characters
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Author : Larry C. Grove
language : en
Publisher: Wiley-Interscience
Release Date : 1997-06-16
Groups And Characters written by Larry C. Grove and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-16 with Mathematics categories.
Grove combines group theory and ordinary character theory in this challenging, self-contained textbook which include many exercises as well as an entire chapter devoted to important and fully detailed examples.
From Groups To Geometry And Back
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Author : Vaughn Climenhaga
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-07
From Groups To Geometry And Back written by Vaughn Climenhaga and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-07 with Mathematics categories.
Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth. The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness. This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009.
Geometry Of Lie Groups
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Author : B. Rosenfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-02-28
Geometry Of Lie Groups written by B. Rosenfeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-28 with Mathematics categories.
This book is the result of many years of research in Non-Euclidean Geometries and Geometry of Lie groups, as well as teaching at Moscow State University (1947- 1949), Azerbaijan State University (Baku) (1950-1955), Kolomna Pedagogical Col lege (1955-1970), Moscow Pedagogical University (1971-1990), and Pennsylvania State University (1990-1995). My first books on Non-Euclidean Geometries and Geometry of Lie groups were written in Russian and published in Moscow: Non-Euclidean Geometries (1955) [Ro1] , Multidimensional Spaces (1966) [Ro2] , and Non-Euclidean Spaces (1969) [Ro3]. In [Ro1] I considered non-Euclidean geometries in the broad sense, as geometry of simple Lie groups, since classical non-Euclidean geometries, hyperbolic and elliptic, are geometries of simple Lie groups of classes Bn and D , and geometries of complex n and quaternionic Hermitian elliptic and hyperbolic spaces are geometries of simple Lie groups of classes An and en. [Ro1] contains an exposition of the geometry of classical real non-Euclidean spaces and their interpretations as hyperspheres with identified antipodal points in Euclidean or pseudo-Euclidean spaces, and in projective and conformal spaces. Numerous interpretations of various spaces different from our usual space allow us, like stereoscopic vision, to see many traits of these spaces absent in the usual space.
Geometry Of Classical Groups Over Finite Fields
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Author : Zhexian Wan
language : en
Publisher:
Release Date : 1993
Geometry Of Classical Groups Over Finite Fields written by Zhexian Wan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Finite fields (Algebra). categories.
This monograph provides a survey of classical groups over finite fields. Many important results, appearing for the first time in book-form, are clearly presented. Most of them have been obtained by the author and students under his supervision.
Representations And Invariants Of The Classical Groups
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Author : Roe Goodman
language : en
Publisher: Cambridge University Press
Release Date : 2000-01-13
Representations And Invariants Of The Classical Groups written by Roe Goodman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-13 with Mathematics categories.
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.
Geometry Of Crystallographic Groups Second Edition
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Author : Andrzej Szczepanski
language : en
Publisher: World Scientific
Release Date : 2024-07-30
Geometry Of Crystallographic Groups Second Edition written by Andrzej Szczepanski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-30 with Mathematics categories.
It is eleven years since the First Edition of Geometry of Crystallographic Groups appeared. This Second Edition expands on the first, providing details of a new result of automorphism of crystallographic groups, and on Hantzsche-Wendt groups/manifolds.Crystalographic groups are groups which act via isometries on some n-dimensional Euclidean space, so-named because in three dimensions they occur as the symmetry groups of a crystal. There are short introductions to the theme before every chapter, and a list of conjectures and open projects at the end of the book.Geometry of Crystallographic Groups is suitable as a textbook for students, containing basic theory of crystallographic groups. It is also suitable for researchers in the field, discussing in its second half more advanced and recent topics.
Geometric Group Theory
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Author : Clara Löh
language : en
Publisher: Springer
Release Date : 2017-12-19
Geometric Group Theory written by Clara Löh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-19 with Mathematics categories.
Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
Classical Topics In Discrete Geometry
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Author : Károly Bezdek
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-23
Classical Topics In Discrete Geometry written by Károly Bezdek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-23 with Mathematics categories.
Geometry is a classical core part of mathematics which, with its birth, marked the beginning of the mathematical sciences. Thus, not surprisingly, geometry has played a key role in many important developments of mathematics in the past, as well as in present times. While focusing on modern mathematics, one has to emphasize the increasing role of discrete mathematics, or equivalently, the broad movement to establish discrete analogues of major components of mathematics. In this way, the works of a number of outstanding mathema- cians including H. S. M. Coxeter (Canada), C. A. Rogers (United Kingdom), and L. Fejes-T oth (Hungary) led to the new and fast developing eld called discrete geometry. One can brie y describe this branch of geometry as the study of discrete arrangements of geometric objects in Euclidean, as well as in non-Euclidean spaces. This, as a classical core part, also includes the theory of polytopes and tilings in addition to the theory of packing and covering. D- crete geometry is driven by problems often featuring a very clear visual and applied character. The solutions use a variety of methods of modern mat- matics, including convex and combinatorial geometry, coding theory, calculus of variations, di erential geometry, group theory, and topology, as well as geometric analysis and number theory.
The Random Matrix Theory Of The Classical Compact Groups
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Author : Elizabeth S. Meckes
language : en
Publisher: Cambridge University Press
Release Date : 2019-08
The Random Matrix Theory Of The Classical Compact Groups written by Elizabeth S. Meckes and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08 with Mathematics categories.
Provides a comprehensive introduction to the theory of random orthogonal, unitary, and symplectic matrices.