Quantum Groups and Their Primitive Ideals

摘要: I. Hopf Algebras.- 1.1 Axioms of a Algebra.- 1.2 Group Algebras and Enveloping 1.3 Adjoint Action.- 1.4 The Dual.- 1.5 Comments Complements.- 2. Excerpts from the Classical Theory.- 2.1 Lie 2.2 Algebraic 2.3 Groups.- 2.4 2.5 3. Encoding Cartan Matrix.- 3.1 Quantum Weyl 3.2 Drinfeld Double.- 3.3 Rosso Form Casimir Invariant.- 3.4 Limit Shapovalev Form.- 3.5 4. Highest Weight Modules.- 4.1 Jantzen Filtration Sum Formula.- 4.2 Kac-Moody 4.3 Integrable Modules for Uq(gc).- 4.4 Demazure Product Formulae.- 4.5 5. Crystal Basis.- 5.1 Operators in Limit.- 5.2 Crystals.- 5.3 Ad-invariant Filtrations, Twisted Actions Basis Uq(n-).- 5.4 Grand Loop.- 5.5 6. Global Bases.- 6.1 ? Operation Embedding Theorem.- 6.2 Globalization.- 6.3 Property.- 6.4 Littelmann's Path 6.5 7. Structure Theorems Uq(g).- 7.1 Local Finiteness 7.2 Positivity 7.3 Separation 7.4 Noetherianity.- 7.5 8. Primitive Spectrum 8.1 Poincare Series Harmonic Space.- 8.2 Factorization PRV Determinants.- 8.3 Verma Module Annihilators.- 8.4 Equivalence Categories.- 8.5 9. Rq[G].- 9.1 Commutativity Relations.- 9.2 Surjectivity Injectivity Theorems.- 9.3 9.4 R-Matrix.- 9.5 10. Prime 10.1 10.2 Group.- 10.3 Ideals 10.4 Algebra Automorphisms.- 10.5 A.2 Ring A.3 Combinatorial Identities Dimension A.4 Remarks on Constructions A.5 Index Notation.