Finiteness Properties Of Arithmetic Groups Acting On Twin Buildings
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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.
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.
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.
Geometry Rigidity and Group Actions
Author | : Robert J. Zimmer,Benson Farb,David Fisher |
Publsiher | : University of Chicago Press |
Total Pages | : 659 |
Release | : 2011-04-15 |
Genre | : Mathematics |
ISBN | : 9780226237893 |
Download Geometry Rigidity and Group Actions Book in PDF, Epub and Kindle
The study of group actions is more than 100 years old but remains a widely studied topic in a variety of mathematic fields. A central development in the last 50 years is the phenomenon of rigidity, whereby one can classify actions of certain groups. This book looks at rigidity.
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.
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.
Buildings
Author | : Peter Abramenko,Kenneth S. Brown |
Publsiher | : Springer Science & Business Media |
Total Pages | : 758 |
Release | : 2008-12-16 |
Genre | : Mathematics |
ISBN | : 9780387788357 |
Download Buildings Book in PDF, Epub and Kindle
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.