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130626  eng 
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a 9780817647179

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a Lusztig, George

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a Introduction to Quantum Groups
h Elektronische Ressource
c by George Lusztig

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a 1st ed. 2010

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a Boston, MA
b Birkhäuser
c 2010, 2010

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a XIV, 352 p
b online resource

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a THE DRINFELD JIMBO ALGERBRA U  The Algebra f  Weyl Group, Root Datum  The Algebra U  The QuasiMatrix  The Symmetries of an Integrable UModule  Complete Reducibility Theorems  Higher Order Quantum Serre Relations  GEOMETRIC REALIZATION OF F  Review of the Theory of Perverse Sheaves  Quivers and Perverse Sheaves  FourierDeligne 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 SimplyLaced 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 PeterWeyl Theorem  The Canonical Topological Basis of  CHANGE OF RINGS  The Algebra  Commutativity Isomorphism  Relation with KacMoody 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

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a Quantum Physics

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a Group Theory and Generalizations

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a Group theory

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a Topological Groups and Lie Groups

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a Lie groups

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a Topological groups

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a Algebra

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a Quantum physics

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a Mathematical physics

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a Mathematical Methods in Physics

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7 
a eng
2 ISO 6392

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b Springer
a Springer eBooks 2005

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a Modern Birkhäuser Classics

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a 10.1007/9780817647179

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u https://doi.org/10.1007/9780817647179?nosfx=y
x Verlag
3 Volltext

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a 512.2

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a Introduction to Quantum Groups will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists, theoretical physicists, and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the work may also be used as a textbook. **************************************** There is no doubt that this volume is a very remarkable piece of work...Its appearance represents a landmark in the mathematical literature. —Bulletin of the London Mathematical Society This book is an important contribution to the field and can be recommended especially to mathematicians working in the field. —EMS Newsletter The present book gives a very efficient presentation of an important part of quantum group theory. It is a valuable contribution to the literature.

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a The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. It is shown that these algebras have natural integral forms that can be specialized at roots of 1 and yield new objects, which include quantum versions of the semisimple groups over fields of positive characteristic. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical bases having rather remarkable properties. This book contains an extensive treatment of the theory of canonical bases in the framework of perverse sheaves. The theory developed in the book includes the case of quantum affine enveloping algebras and, more generally, the quantum analogs of the Kac–Moody Lie algebras.

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a —Mededelingen van het Wiskundig Lusztig's book is very well written and seems to be flawless...Obviously, this will be the standard reference book for the material presented and anyone interested in the Drinfeld–Jimboalgebras will have to study it very carefully. —ZAA [T]his book is much more than an 'introduction to quantum groups.' It contains a wealth of material. In addition to the many important results (of which several are new–at least in the generality presented here), there are plenty of useful calculations (commutator formulas, generalized quantum Serre relations, etc.). —Zentralblatt MATH.
