Alphabeta MathQuasitriangular Hopf Algebras and Braided Module Categories
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1 · Prerequisites
Abstract Algebra
- Binary Operations, Monoids, Groups and Subgroups
- Chain Conditions, Semisimple Modules and the Wedderburn–Artin Theorem
- Cosets, Index and Lagrange's Theorem
- Free Modules, Exact Sequences, Projective and Injective Modules
- Group Homomorphisms and the Isomorphism Theorems
- Ideals, Quotient Rings and the Isomorphism Theorems for Rings
- Modules, Submodules, Quotient Modules and the Isomorphism Theorems
- Normal Subgroups and Quotient Groups
- Rings, Subrings, Integral Domains and Fields
- Tensor Products of Modules
Categorification and Geometric Representation Theory
Linear Algebra
Real Analysis
2 · Logical flowchart
3 · Items
Lemma
Regular tensor-algebra multiplication is detected at the unit tensor
Definition
Leg notation and quasitriangular Hopf algebras
Lemma
Counit normalization and the Yang–Baxter identity for a quasitriangular structure
Definition
Braiding on the module category and triangular structures
Theorem
A quasitriangular structure gives and is recovered from a module braiding
Lemma