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Modular representation theory

Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups over a field K of positive characteristic p, necessarily a prime number. As well as having applications to group theory, modular representations arise naturally in other branches of mathematics, such as…

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Example

Ring theory interpretation

Reduction (mod p)

Number of simple modules

Blocks and the structure of the group algebra

Projective modules

  • Socle Socle (mathematics)

Decomposition matrix and Cartan matrix

Defect groups

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Modular representation theory

Nodes76
Edges75
Triples21
Avg. degree1.97
Density0.026316
Components1

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Modular representation theory

Top relations

related to Blocks and the structure of the group algebra · 8
Modular representation theory → Brauer, Each, For, In, Maschke's, The, To, When
related to Brauer characters · 6
Modular representation theory → Brauer, Modular, Once, Richard Brauer, Such, When
related to Reduction (mod p) · 6
Modular representation theory → Brauer, Each, In, On, The, Those
is a · 1
Modular representation theory → branch of mathematics

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Important terminology

group brauer characteristic theory block order projective representation finite module indecomposable simple ordinary modules defect modular algebra irreducible characters matrix

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Modular representation theoryis abranch of mathematics0.90text
Modular representation theoryrelated to Blocks and the structure of the group algebraIn0.60section
Modular representation theoryrelated to Blocks and the structure of the group algebraMaschke's0.60section
Modular representation theoryrelated to Blocks and the structure of the group algebraWhen0.60section
Modular representation theoryrelated to Blocks and the structure of the group algebraTo0.60section
Modular representation theoryrelated to Blocks and the structure of the group algebraThe0.60section
Modular representation theoryrelated to Blocks and the structure of the group algebraFor0.60section
Modular representation theoryrelated to Blocks and the structure of the group algebraEach0.60section
Modular representation theoryrelated to Blocks and the structure of the group algebraBrauer0.60section
Modular representation theoryrelated to Brauer charactersModular0.60section
Modular representation theoryrelated to Brauer charactersRichard Brauer0.60section
Modular representation theoryrelated to Brauer charactersSuch0.60section

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