Arithmetic Groups And Their Generalizations
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Arithmetic Groups And Their Generalizations
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Author : Lizhen Ji
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Arithmetic Groups And Their Generalizations written by Lizhen Ji 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 2008 with Mathematics categories.
In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as $\mathbf{Z}$ or $\textrm{SL}(n, \mathbf{Z})$. Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics. Titles in this series are co-published with International Press, Cambridge, MA.Table of Contents: Introduction; General comments on references; Examples of basic arithmetic groups; General arithmetic subgroups and locally symmetric spaces; Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups; Different completions of $\mathbb{Q}$ and $S$-arithmetic groups over number fields; Global fields and $S$-arithmetic groups over function fields; Finiteness properties of arithmetic and $S$-arithmetic groups; Symmetric spaces, Bruhat-Tits buildings and their arithmetic quotients; Compactifications of locally symmetric spaces; Rigidity of locally symmetric spaces; Automorphic forms and automorphic representations for general arithmetic groups; Cohomology of arithmetic groups; $K$-groups of rings of integers and $K$-groups of group rings; Locally homogeneous manifolds and period domains; Non-cofinite discrete groups, geometrically finite groups; Large scale geometry of discrete groups; Tree lattices; Hyperbolic groups; Mapping class groups and outer automorphism groups of free groups; Outer automorphism group of free groups and the outer spaces; References; Index. Review from Mathematical Reviews: ...the author deserves credit for having done the tremendous job of encompassing every aspect of arithmetic groups visible in today's mathematics in a systematic manner; the book should be an important guide for some time to come.(AMSIP/43.
Arithmetic Groups
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Author : James E. Humphreys
language : en
Publisher:
Release Date : 1980
Arithmetic Groups written by James E. Humphreys and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Arithmetic groups categories.
Algebraic Groups And Their Generalizations Quantum And Infinite Dimensional Methods
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Author : William Joseph Haboush
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Algebraic Groups And Their Generalizations Quantum And Infinite Dimensional Methods written by William Joseph Haboush 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 1994 with Mathematics categories.
Proceedings of a research institute held at Pennsylvania State University, July 1991, focusing on quantum and infinite-dimensional methods of algebraic groups. Topics include perverse sheaves, finite Chevalley groups, the general theory of algebraic groups, representations, invariant theory, general
Algebraic Groups And Their Generalizations Classical Methods
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Author : William Joseph Haboush
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Algebraic Groups And Their Generalizations Classical Methods written by William Joseph Haboush 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 1994 with Mathematics categories.
Introduction To Arithmetic Groups
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Author : Armand Borel
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-11-07
Introduction To Arithmetic Groups written by Armand Borel 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 2019-11-07 with Education categories.
Fifty years after it made the transition from mimeographed lecture notes to a published book, Armand Borel's Introduction aux groupes arithmétiques continues to be very important for the theory of arithmetic groups. In particular, Chapter III of the book remains the standard reference for fundamental results on reduction theory, which is crucial in the study of discrete subgroups of Lie groups and the corresponding homogeneous spaces. The review of the original French version in Mathematical Reviews observes that “the style is concise and the proofs (in later sections) are often demanding of the reader.” To make the translation more approachable, numerous footnotes provide helpful comments.
Twin Buildings And Applications To S Arithmetic Groups
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Author : Peter Abramenko
language : en
Publisher: Springer
Release Date : 2006-11-14
Twin Buildings And Applications To S Arithmetic Groups written by Peter Abramenko and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This book is addressed to mathematicians and advanced students interested in buildings, groups and their interplay. Its first part introduces - presupposing good knowledge of ordinary buildings - the theory of twin buildings, discusses its group-theoretic background (twin BN-pairs), investigates geometric aspects of twin buildings and applies them to determine finiteness properties of certain S-arithmetic groups. This application depends on topological properties of some subcomplexes of spherical buildings. The background of this problem, some examples and the complete solution for all "sufficiently large" classical buildings are covered in detail in the second part of the book.
Normal 2 Coverings Of The Finite Simple Groups And Their Generalizations
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Author : Daniela Bubboloni
language : en
Publisher: Springer Nature
Release Date : 2024-07-22
Normal 2 Coverings Of The Finite Simple Groups And Their Generalizations written by Daniela Bubboloni and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-22 with Mathematics categories.
This book provides a complete and comprehensive classification of normal 2-coverings of non-abelian simple groups and their generalizations. While offering readers a thorough understanding of these structures, and of the groups admitting them, it delves into the properties of weak normal coverings. The focal point is the weak normal covering number of a group G, the minimum number of proper subgroups required for every element of G to have a conjugate within one of these subgroups, via an element of Aut(G). This number is shown to be at least 2 for every non-abelian simple group and the non-abelian simple groups for which this minimum value is attained are classified. The discussion then moves to almost simple groups, with some insights into their weak normal covering numbers. Applications span algebraic number theory, combinatorics, Galois theory, and beyond. Compiling existing material and synthesizing it into a cohesive framework, the book gives a complete overview of this fundamental aspect of finite group theory. It will serve as a valuable resource for researchers and graduate students working on non-abelian simple groups,
Extensions Of The Stability Theorem Of The Minkowski Space In General Relativity
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Author : Lydia Bieri
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-06-30
Extensions Of The Stability Theorem Of The Minkowski Space In General Relativity written by Lydia Bieri 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 2009-06-30 with Mathematics categories.
A famous result of Christodoulou and Klainerman is the global nonlinear stability of Minkowski spacetime. In this book, Bieri and Zipser provide two extensions to this result. In the first part, Bieri solves the Cauchy problem for the Einstein vacuum equations with more general, asymptotically flat initial data, and describes precisely the asymptotic behavior. In particular, she assumes less decay in the power of $r$ and one less derivative than in the Christodoulou-Klainerman result. She proves that in this case, too, the initial data, being globally close to the trivial data, yields a solution which is a complete spacetime, tending to the Minkowski spacetime at infinity along any geodesic. In contrast to the original situation, certain estimates in this proof are borderline in view of decay, indicating that the conditions in the main theorem on the decay at infinity on the initial data are sharp. In the second part, Zipser proves the existence of smooth, global solutions to the Einstein-Maxwell equations. A nontrivial solution of these equations is a curved spacetime with an electromagnetic field. To prove the existence of solutions to the Einstein-Maxwell equations, Zipser follows the argument and methodology introduced by Christodoulou and Klainerman. To generalize the original results, she needs to contend with the additional curvature terms that arise due to the presence of the electromagnetic field $F$; in her case the Ricci curvature of the spacetime is not identically zero but rather represented by a quadratic in the components of $F$. In particular the Ricci curvature is a constant multiple of the stress-energy tensor for $F$. Furthermore, the traceless part of the Riemann curvature tensor no longer satisfies the homogeneous Bianchi equations but rather inhomogeneous equations including components of the spacetime Ricci curvature. Therefore, the second part of this book focuses primarily on the derivation of estimates for the new terms that arise due to the presence of the electromagnetic field.
Moonshine The Monster And Related Topics
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Author : Chongying Dong
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Moonshine The Monster And Related Topics written by Chongying Dong 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 1996 with Mathematics categories.
This is the proceedings of a Joint Summer Research Conference held at Mount Holyoke College in Jun 1994. As perhaps the first conference proceedings devoted exclusively to the subject known as "Moonshine", this work contains something for many mathematicians and physicists. Many of the results featured are not available elsewhere.
Heat Kernel And Analysis On Manifolds
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Author : Alexander Grigoryan
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Heat Kernel And Analysis On Manifolds written by Alexander Grigoryan 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 2009 with Mathematics categories.
"This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincaré Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and p -Laplace operators, heat kernel and spherical inversion on SL 2 (C) , random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs."--Publisher's website.