Alphabeta MathHow 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.
Jordan–Chevalley parts under the adjoint representation
Remark
The compatibility between the abstract Jordan decomposition of Abstract Jordan decomposition and the operator decomposition supplied by The additive Jordan–Chevalley supplier is proof-bearing. It is therefore not imported as a convention or as part of a definition: it is proved in Jordan–Chevalley parts agree under the adjoint representation, which precedes every consumer of the compatibility on this page, and the internal existence and uniqueness theorem Jordan decomposition lies inside a complex semisimple Lie algebra then rests on it rather than on an appeal to the operator theorem alone.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Anthony W. Knapp, Lie Groups Beyond an Introduction, 2nd ed., Chapter II (standard reference, not scraped)