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Brauer homomorphism for a p subgroup
Definition
Let be finite, the characteristic- residue field from p-blocks from primitive central idempotents, and a -subgroup. On the conjugation-fixed algebra define This coefficient projection is called the Brauer map. The next theorem proves it is a unital surjective algebra homomorphism on this domain. No multiplicativity is asserted on all of . For it is the identity.
Sources
Webb, A Course in Finite Group Representation Theory, §§11.3, 11.6 and 12.3–12.5, especially pp.240–245. Local argument and conventions as displayed above.
Depends on
Used by
- Relative Brauer homomorphism Definition
- Brauer correspondence for a defect-D8 block of S7 in characteristic 2 Example
- A global block of defect D determines a local block of defect D Lemma
- Brauer homomorphism is conjugation equivariant Lemma
- Brauer images retain the surviving primitive idempotents Lemma
- Brauer kernel and relative trace support Lemma
- Every local full-defect block induces to a global block of defect D Lemma
- Normal p-subgroups fix block idempotents under Brauer projection Lemma
- Brauer homomorphism is multiplicative Theorem
- Maximal Brauer pairs exist and are conjugate Theorem
Dependency tree · two levels
2 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
- Webb, A Course in Finite Group Representation Theory, §§11.3, 11.6 and 12.3–12.5, especially pp.240–245 (standard reference, not scraped)