دانلود کتاب Introduction to Quantum Groups

فهرست مطالب :

Preface
Contents
Part I Quantum Groups
Chapter 1 Quantum Spaces
1.1 Operator Algebras
1.2 Gelfand’s Theorem
1.3 Algebraic Manifolds
1.4 Axiomatization Fix
1.5 Exercises
Chapter 2 Quantum Groups
2.1 Hopf Algebras
2.2 Axioms, Theory
2.3 Product Operations
2.4 Free Constructions
2.5 Exercises
Chapter 3 Representation Theory
3.1 Representations
3.2 Peter–Weyl Theory
3.3 The Haar Measure
3.4 More Peter–Weyl
3.5 Exercises
Chapter 4 Tannakian Duality
4.1 Tensor Categories
4.2 Abstract Algebra
4.3 The Correspondence
4.4 Brauer Theorems
4.5 Exercises
Part II Quantum Rotations
Chapter 5 Free Rotations
5.1 Gram Determinants
5.2 TheWigner Law
5.3 Clebsch–Gordan Rules
5.4 Symplectic Groups
5.5 Exercises
Chapter 6 Unitary Groups
6.1 Gaussian Laws
6.2 Circular Variables
6.3 Fusion Rules
6.4 Further Results
6.5 Exercises
Chapter 7 Easiness, Twisting
7.1 Partitions, Easiness
7.2 Basic Operations
7.3 Ad-Hoc Twisting
7.4 Schur–Weyl Twisting
7.5 Exercises
Chapter 8 Probabilistic Aspects
8.1 Free Probability
8.2 Laws of Characters
8.3 Truncated Characters
8.4 Gram Determinants
8.5 Exercises
Part III Quantum Permutations
Chapter 9 Quantum Permutations
9.1 Magic Matrices
9.2 Representations
9.3 Twisted Extension
9.4 Poisson Laws
9.5 Exercises
Chapter 10 Quantum Reflections
10.1 Finite Graphs
10.2 Reflection Groups
10.3 Complex Reflections
10.4 Bessel Laws
10.5 Exercises
Chapter 11 Classification Results
11.1 Uniform Groups
11.2 Twistability
11.3 Orientability
11.4 Ground Zero
11.5 Exercises
Chapter 12 The Standard Cube
12.1 Face Results
12.2 Edge Results
12.3 Beyond Easiness
12.4 Maximality Questions
12.5 Exercises
Part IV Advanced Topics
Chapter 13 Toral Subgroups
13.1 Diagonal Tori
13.2 The Skeleton
13.3 Generation Questions
13.4 Fourier Liberation
13.5 Exercises
Chapter 14 Amenability, Growth
14.1 Functional Analysis
14.2 Amenability
14.3 Growth
14.4 Toral Conjectures
14.5 Exercises
Chapter 15 Homogeneous Spaces
15.1 Quotient Spaces
15.2 Partial Isometries
15.3 Free Isometries
15.4 Integration Theory
15.5 Exercises
Chapter 16 Modeling Questions
16.1 Matrix Models
16.2 Stationarity
16.3 Weyl Matrices
16.4 Fourier Models
16.5 Exercises
References
Index