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.

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p-blocks from primitive central idempotents

Definition

Fix a splitting $p$ -modular system $(K, O, k)$ for a finite group $G$ . A $p$ -block idempotent is a primitive central idempotent of $O G$ or, after reduction, of $k G$ .

If $e$ is such an idempotent, the corresponding block is the two-sided ideal

$B = O G e or B = k G e .$

The primitive central idempotents are pairwise orthogonal and sum to $1$ , so the algebra splits as a direct product of its block summands.

Depends on

A splitting p-modular system for a finite group is a p-modular system whose fraction and residue fields split the needed group algebras

Used by

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

J. Miquel Martinez, Modular Representation Theory of Finite Groups (standard reference, not scraped)
Tudor Ciurca, Representation Theory (standard reference, not scraped)