Alphabeta MathVertices Sources and the Green Correspondence
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The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
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 Actions, Orbits, Stabilisers and Cayley's Theorem
- Group Homomorphisms and the Isomorphism Theorems
- Induced Representations, Frobenius Reciprocity and Applications
- Modules, Submodules, Quotient Modules and the Isomorphism Theorems
- Normal Subgroups and Quotient Groups
- Rings, Subrings, Integral Domains and Fields
- Tensor Products of Modules
- The Group Algebra and Representations of Finite Groups
Group Theory
Linear Algebra
Real Analysis
Representation Theory of Groups
2 · Logical flowchart
3 · Items
Definition
Green exceptional intersection families
Lemma
Green exceptional family containment and fusion
Lemma
Green vertex retention and inducing lift
Lemma
Green mackey intersections force proper vertices
Lemma
Green restriction has one distinguished summand
Lemma
Green induction has one distinguished summand
Lemma
Green distinguished summands are mutually inverse
Theorem
Green correspondence with exceptional families
Corollary