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...
保存先:
| 第一著者: | |
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| フォーマット: | Livre numérique |
| 言語: | Anglais |
| 出版事項: |
Boston, MA :
Birkhäuser Boston
[20..].
Cham : Springer Nature |
| 版: | 1st ed. 2010. |
| シリーズ: | Modern Birkhäuser Classics
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| 主題: | |
| オンライン･アクセス: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| 注記: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Introduction to quantum groups, George Lusztig, Reprint of the 1994 edition, 2010, Boston (Mass.), Birkhäuser, 1 vol. (XIV-340 p.), Modern Birkhäuser Classics, 978-0-8176-4716-2 • Introduction to quantum groups, George Lusztig, 1993, Boston (Mass.), Birkhäuser, 1 volume (XII-340 pages), Progress in mathematics, 3-7643-3712-5 |
目次:
- 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