DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-05

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.

Regular elements and rank for a complex semisimple Lie algebra

Definition

Let $g$ be a complex semisimple Lie algebra. For $x \in g$ , let

$C_{g} (x) : = {y \in g : [x, y] = 0}$

be its centralizer. The minimum possible dimension of $C_{g} (x)$ is called the rank of $g$ and is denoted $rank g$ . An element $x \in g$ is regular when

$\dim C_{g} (x) = rank g .$

Used by

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Pavel Etingof, Lie Groups and Lie Algebras I (standard reference, not scraped)