DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-14

How statement and proof provenance work

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.

Homomorphisms of possibly infinite-dimensional Lie algebras

Definition

Let $g$ and $h$ be Lie algebras over the same field $k$ , with no dimension restriction. A Lie-algebra homomorphism $f : g \to h$ is a linear map (Linear map between vector spaces over the same field) satisfying

$f ([x, y]) = [f (x), f (y)]$

for all $x, y \in g$ . A bijective Lie-algebra homomorphism is an isomorphism; its inverse preserves brackets because applying $f$ reduces that assertion to bracket preservation by $f$ .

Depends on

Dependency tree · 2 levels

Sources

Etingof, MIT 18.745 notes, §3.2