Alphabeta MathYangians, Quantum Affine Algebras, and Transfer Matrices
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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
- 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
Definition
The type-A RTT Yangian in the rational i-normalization
Lemma
The RTT relation has an explicit component commutator form
Proposition
The RTT Yangian has its standard Hopf structure
Definition
Evaluation modules of the type-A RTT Yangian
Theorem
The gl_N evaluation formula satisfies RTT
Lemma
The rational i-normalization is the standard RTT normalization after rescaling
Proposition
The type-A rational R-matrix satisfies Yang–Baxter and has exact singular parameters
Lemma
The rational R-matrix intertwines two fundamental evaluation orders
Definition
Finite periodic fundamental evaluation chain and transfer matrix
Lemma
The periodic fundamental monodromy satisfies RTT
Theorem
Finite periodic transfer matrices commute
Lemma