Discrete Subgroups Of Lie Groups

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Discrete Subgroups Of Semisimple Lie Groups

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Author : Gregori A. Margulis
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-02-15

Discrete Subgroups Of Semisimple Lie Groups written by Gregori A. Margulis 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 1991-02-15 with Mathematics categories.

Discrete subgroups have played a central role throughout the development of numerous mathematical disciplines. Discontinuous group actions and the study of fundamental regions are of utmost importance to modern geometry. Flows and dynamical systems on homogeneous spaces have found a wide range of applications, and of course number theory without discrete groups is unthinkable. This book, written by a master of the subject, is primarily devoted to discrete subgroups of finite covolume in semi-simple Lie groups. Since the notion of "Lie group" is sufficiently general, the author not only proves results in the classical geometry setting, but also obtains theorems of an algebraic nature, e.g. classification results on abstract homomorphisms of semi-simple algebraic groups over global fields. The treatise of course contains a presentation of the author's fundamental rigidity and arithmeticity theorems. The work in this monograph requires the language and basic results from fields such as algebraic groups, ergodic theory, the theory of unitary representatons, and the theory of amenable groups. The author develops the necessary material from these subjects; so that, while the book is of obvious importance for researchers working in related areas, it is essentially self-contained and therefore is also of great interest for advanced students.

Discrete Subgroups Of Lie Groups

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Author : Madabusi S. Raghunathan
language : en
Publisher: Springer
Release Date : 2012-11-09

Discrete Subgroups Of Lie Groups written by Madabusi S. Raghunathan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-09 with Mathematics categories.

This book originated from a course of lectures given at Yale University during 1968-69 and a more elaborate one, the next year, at the Tata Institute of Fundamental Research. Its aim is to present a detailed ac count of some of the recent work on the geometric aspects of the theory of discrete subgroups of Lie groups. Our interest, by and large, is in a special class of discrete subgroups of Lie groups, viz., lattices (by a lattice in a locally compact group G, we mean a discrete subgroup H such that the homogeneous space GJ H carries a finite G-invariant measure). It is assumed that the reader has considerable familiarity with Lie groups and algebraic groups. However most of the results used frequently in the book are summarised in "Preliminaries"; this chapter, it is hoped, will be useful as a reference. We now briefly outline the contents of the book. Chapter I deals with results of a general nature on lattices in locally compact groups. The second chapter is an account of the fairly complete study of lattices in nilpotent Lie groups carried out by Ma1cev. Chapters III and IV are devoted to lattices in solvable Lie groups; most of the theorems here are due to Mostow. In Chapter V we prove a density theorem due to Borel: this is the first important result on lattices in semisimple Lie groups.

Discrete Subgroups Of Lie Groups

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Author : M. S. Raghunathan
language : de
Publisher:
Release Date : 1972

Discrete Subgroups Of Lie Groups written by M. S. Raghunathan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.

Discrete Subgroups Of Lie Groups And Applications To Moduli

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Author : Walter L. Baily
language : en
Publisher: Oxford University Press, USA
Release Date : 1975

Discrete Subgroups Of Lie Groups And Applications To Moduli written by Walter L. Baily and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.

"This book contains the original papers presented at an International Cooloquium on Discrete Subgroups of Lie Groups and Applications to Moduli held at the Tata Institute of Fundamental Research in January 1973" -- Back cover.

Introduction To Lie Groups And Lie Algebras

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Author :
language : en
Publisher: Academic Press
Release Date : 1973-04-18

Introduction To Lie Groups And Lie Algebras written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-04-18 with Mathematics categories.

Introduction to Lie groups and Lie algebras

Continuous Cohomology Discrete Subgroups And Representations Of Reductive Groups

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Author : Armand Borel
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-11-21

Continuous Cohomology Discrete Subgroups And Representations Of Reductive 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 2013-11-21 with Mathematics categories.

It has been nearly twenty years since the first edition of this work. In the intervening years, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups. This second edition is a corrected and expanded version of the original, which was an important catalyst in the expansion of the field. Besides the fundamental material on cohomology and discrete subgroups present in the first edition, this edition also contains expositions of some of the most important developments of the last two decades.

Lie Groups And Lie Algebras Ii

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Author : A.L. Onishchik
language : en
Publisher: Boom Koninklijke Uitgevers
Release Date : 2000-02-03

Lie Groups And Lie Algebras Ii written by A.L. Onishchik and has been published by Boom Koninklijke Uitgevers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-03 with Mathematics categories.

A systematic survey of all the basic results on the theory of discrete subgroups of Lie groups, presented in a convenient form for users. The book makes the theory accessible to a wide audience, and will be a standard reference for many years to come.

Geometry Analysis And Topology Of Discrete Groups

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Author : Lizhen Ji
language : en
Publisher:
Release Date : 2008

Geometry Analysis And Topology Of Discrete Groups written by Lizhen Ji and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

Presents 15 papers treating discrete groups as they occur in areas such as algebra, analysis, geometry, number theory and topology. This work helps graduate students and researchers to understand the structures and applications of discrete subgroups of Lie groups and locally symmetric spaces.

Dynamics Geometry Number Theory

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Author : David Fisher
language : en
Publisher: University of Chicago Press
Release Date : 2022-02-07

Dynamics Geometry Number Theory written by David Fisher and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-07 with Mathematics categories.

"Mathematicians David Fisher, Dmitry Kleinbock, and Gregory Soifer highlight in this edited collection the foundations and evolution of research by mathematician Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics. Margulis' ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. The broad goal of this volume is to introduce these areas, their development, their use in current research, and the connections between them. The foremost experts on the topic have written each of the chapters in this volume with a view to making them accessible by graduate students and by experts in other parts of mathematics"--