Introduction to Quantum Groups

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...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Lusztig, George (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2010.
Edición:1st ed. 2010.
Colección:Modern Birkhäuser Classics,
Temas:
Group theory.
Quantum physics.
Topological groups.
Lie groups.
Algebra.
Mathematical physics.
Group Theory and Generalizations.
Quantum Physics.
Topological Groups and Lie Groups.
Mathematical Methods in Physics.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

Ejemplares similares