Twin Buildings And Applications To S Arithmetic Groups
Download Twin Buildings And Applications To S Arithmetic Groups full books in PDF, epub, and Kindle. Read online free Twin Buildings And Applications To S Arithmetic Groups ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Twin Buildings and Applications to S Arithmetic Groups
Author | : Peter Abramenko |
Publsiher | : Springer |
Total Pages | : 131 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 9783540495703 |
Download Twin Buildings and Applications to S Arithmetic Groups Book in PDF, Epub and Kindle
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.
Buildings Finite Geometries and Groups
Author | : N.S. Narasimha Sastry |
Publsiher | : Springer Science & Business Media |
Total Pages | : 348 |
Release | : 2011-11-13 |
Genre | : Mathematics |
ISBN | : 9781461407096 |
Download Buildings Finite Geometries and Groups Book in PDF, Epub and Kindle
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.
Finiteness Properties of Arithmetic Groups Acting on Twin Buildings
Author | : Stefan Witzel |
Publsiher | : Springer |
Total Pages | : 128 |
Release | : 2014-07-16 |
Genre | : Mathematics |
ISBN | : 9783319064772 |
Download Finiteness Properties of Arithmetic Groups Acting on Twin Buildings Book in PDF, Epub and Kindle
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.
Arithmetic Groups and Their Generalizations
Author | : Lizhen Ji |
Publsiher | : American Mathematical Soc. |
Total Pages | : 282 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9780821848661 |
Download Arithmetic Groups and Their Generalizations Book in PDF, Epub and Kindle
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
Author | : Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk |
Publsiher | : Cambridge University Press |
Total Pages | : 379 |
Release | : 2023-08-31 |
Genre | : Mathematics |
ISBN | : 9780521113618 |
Download Algebraic Groups and Number Theory Book in PDF, Epub and Kindle
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
Author | : Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk |
Publsiher | : Cambridge University Press |
Total Pages | : 380 |
Release | : 2023-08-31 |
Genre | : Mathematics |
ISBN | : 9781009380652 |
Download Algebraic Groups and Number Theory Volume 1 Book in PDF, Epub and Kindle
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
Author | : Thomas Wolfgang Müller |
Publsiher | : Cambridge University Press |
Total Pages | : 608 |
Release | : 2004-04-08 |
Genre | : Mathematics |
ISBN | : 0521542871 |
Download Groups Book in PDF, Epub and Kindle
Survey and research articles from the Bielefeld conference on topological, combinatorial and arithmetic aspects of groups.
Homogeneous Spaces Tits Buildings and Isoparametric Hypersurfaces
Author | : Linus Kramer |
Publsiher | : American Mathematical Soc. |
Total Pages | : 114 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9780821829066 |
Download Homogeneous Spaces Tits Buildings and Isoparametric Hypersurfaces Book in PDF, Epub and Kindle
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