Twin Buildings And Applications To S Arithmetic Groups
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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.
Finiteness Properties Of Arithmetic Groups Acting On Twin Buildings
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Author : Stefan Witzel
language : en
Publisher: Springer
Release Date : 2014-07-16
Finiteness Properties Of Arithmetic Groups Acting On Twin Buildings written by Stefan Witzel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-16 with Mathematics categories.
Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places. While the proof of the general Rank Theorem uses an involved reduction theory due to Harder, by imposing the restrictions that the group is split and that S has only two places, one can instead make use of the theory of twin buildings.
Buildings Finite Geometries And Groups
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Author : N.S. Narasimha Sastry
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-13
Buildings Finite Geometries And Groups written by N.S. Narasimha Sastry 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 2011-11-13 with Mathematics categories.
This is the Proceedings of the ICM 2010 Satellite Conference on “Buildings, Finite Geometries and Groups” organized at the Indian Statistical Institute, Bangalore, during August 29 – 31, 2010. This is a collection of articles by some of the currently very active research workers in several areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lie theory, etc. These articles reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective the authors bring in their articles on the current developments and the major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these areas.
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.
Algebraic Groups And Number Theory
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Author : Vladimir Platonov
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-31
Algebraic Groups And Number Theory written by Vladimir Platonov 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 2023-08-31 with Mathematics categories.
The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.
Algebraic Groups And Number Theory Volume 1
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Author : Vladimir Platonov
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-31
Algebraic Groups And Number Theory Volume 1 written by Vladimir Platonov 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 2023-08-31 with Mathematics categories.
The first edition of this book provided the first systematic exposition of the arithmetic theory of algebraic groups. This revised second edition, now published in two volumes, retains the same goals, while incorporating corrections and improvements, as well as new material covering more recent developments. Volume I begins with chapters covering background material on number theory, algebraic groups, and cohomology (both abelian and non-abelian), and then turns to algebraic groups over locally compact fields. The remaining two chapters provide a detailed treatment of arithmetic subgroups and reduction theory in both the real and adelic settings. Volume I includes new material on groups with bounded generation and abstract arithmetic groups. With minimal prerequisites and complete proofs given whenever possible, this book is suitable for self-study for graduate students wishing to learn the subject as well as a reference for researchers in number theory, algebraic geometry, and related areas.
Groups
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Author : Thomas Wolfgang Müller
language : en
Publisher: Cambridge University Press
Release Date : 2004-04-08
Groups written by Thomas Wolfgang Müller 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 2004-04-08 with Mathematics categories.
Survey and research articles from the Bielefeld conference on topological, combinatorial and arithmetic aspects of groups.
Tits Buildings And The Model Theory Of Groups
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Author : Katrin Tent
language : en
Publisher: Cambridge University Press
Release Date : 2002-01-03
Tits Buildings And The Model Theory Of Groups written by Katrin Tent 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 2002-01-03 with Mathematics categories.
Introduction to buildings and their geometries with emphasis on model theoretic constructions, covering recent developments.
Buildings
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Author : Peter Abramenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-16
Buildings written by Peter Abramenko 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 2008-12-16 with Mathematics categories.
This book treats Jacques Tit's beautiful theory of buildings, making that theory accessible to readers with minimal background. It covers all three approaches to buildings, so that the reader can choose to concentrate on one particular approach. Beginners can use parts of the new book as a friendly introduction to buildings, but the book also contains valuable material for the active researcher. This book is suitable as a textbook, with many exercises, and it may also be used for self-study.
Homogeneous Spaces Tits Buildings And Isoparametric Hypersurfaces
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Author : Linus Kramer
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Homogeneous Spaces Tits Buildings And Isoparametric Hypersurfaces written by Linus Kramer 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 2002 with Mathematics categories.
This title classifys 1-connected compact homogeneous spaces which have the same rational cohomology as a product of spheres $\mahtbb{S} DEGREES{n_1}\times\mathbb{S} DEGREES{n_2}$, with $3\leq n_1\leq n_2$ and $n_2$ odd. As an application, it classifys compact generalized quadrangles (buildings of type $C_2)$ which admit a point transitive automorphism group, and isoparametric hypersurfaces which admit a transitive isometry group on one f