TY  - BOOK
AU  - Borel,Armand
AU  - Pham,Lam Laurent
AU  - Morris,Dave Witte
TI  - Introduction to arithmetic groups
T2  - University lecture series,
SN  - 9781470452315
U1  - 512.743 
PY  - 2019///
CY  - Rhode Island
PB  - American Mathematical Society
KW  - Linear algebraic groups
KW  - Group theory
KW  - Set theory
N1  - Originally published in French: Introduction aux groupes arithmétiques / Armand Borel (Paris : Hermann, 1969); Includes bibliographical references (pages 115-116) and index
N2  - This book provides a gentle introduction to the study of arithmetic subgroups of semisimple Lie groups. This means that the goal is to understand the group SL(n,Z) and certain of its subgroups. Among the major results discussed in the later chapters are the Mostow Rigidity Theorem, the Margulis Superrigidity Theorem, Ratner's Theorems, and the classification of arithmetic subgroups of classical groups. As background for the proofs of these theorems, the book provides primers on lattice subgroups, arithmetic groups, real rank and Q-rank, ergodic theory, unitary representations, amenability, Kazhdan's property (T), and quasi-isometries. Numerous exercises enhance the book's usefulness both as a textbook for a second-year graduate course and for self-study. In addition, notes at the end of each chapter have suggestions for further reading. (Proofs in this book often consider only an illuminating special case.) Readers are expected to have some acquaintance with Lie groups, but appendices briefly review the prerequisite background
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ER  -