Autor: George Lusztig
ISBN-13: 9780817647162
Einband: Taschenbuch
Seiten: 340
Gewicht: 541 g
Format: 233x159x25 mm
Sprache: Englisch

Introduction to Quantum Groups

Modern Birkhäuser Classics
 Taschenbuch
70,83 €*
InhaltsangabePreface.- Part I: The Drinfeld-Jimbo Algebra U.- Part II: Geometric Realization of f.- Part III: Kashiwara's Operators and Applications.- Part IV: Canonical Basis of U.- Part V: Change of Rings.- Part VI: Braid Group Action.- Index of Notation.- Index of Terminology.
THE DRINFELD JIMBO ALGERBRA U.- The Algebra f.- Weyl Group, Root Datum.- The Algebra U.- The Quasi--Matrix.- The Symmetries of an Integrable U-Module.- Complete Reducibility Theorems.- Higher Order Quantum Serre Relations.- GEOMETRIC REALIZATION OF F.- Review of the Theory of Perverse Sheaves.- Quivers and Perverse Sheaves.- Fourier-Deligne Transform.- Periodic Functors.- Quivers with Automorphisms.- The Algebras and k.- The Signed Basis of f.- KASHIWARAS OPERATIONS AND APPLICATIONS.- The Algebra .- Kashiwara's Operators in Rank 1.- Applications.- Study of the Operators .- Inner Product on .- Bases at ?.- Cartan Data of Finite Type.- Positivity of the Action of Fi, Ei in the Simply-Laced Case.- CANONICAL BASIS OF U.- The Algebra .- Canonical Bases in Certain Tensor Products.- The Canonical Basis .- Inner Product on .- Based Modules.- Bases for Coinvariants and Cyclic Permutations.- A Refinement of the Peter-Weyl Theorem.- The Canonical Topological Basis of .- CHANGE OF RINGS.- The Algebra .- Commutativity Isomorphism.- Relation with Kac-Moody Lie Algebras.- Gaussian Binomial Coefficients at Roots of 1.- The Quantum Frobenius Homomorphism.- The Algebras .- BRAID GROUP ACTION.- The Symmetries of U.- Symmetries and Inner Product on f.- Braid Group Relations.- Symmetries and U+.- Integrality Properties of the Symmetries.- The ADE Case.
The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.
Autor: George Lusztig
ISBN-13 :: 9780817647162
ISBN: 0817647163
Erscheinungsjahr: 01.01.2011
Verlag: Springer Basel AG
Gewicht: 541g
Seiten: 340
Sprache: Englisch
Auflage Reprint of the 1994 Edition
Sonstiges: Taschenbuch, 233x159x25 mm, 14 black & white illustrations, 14 black & white line drawings