Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Modular_representation_theory> ?p ?o }
- Modular_representation_theory abstract "Modular representation theory is a branch of mathematics, and that part of representation theory that studies linear representations of finite groups over a field K of positive characteristic. As well as having applications to group theory, modular representations arisenaturally in other branches of mathematics, such as algebraic geometry, coding theory, combinatorics and number theory.Within finite group theory, character-theoretic results provedby Richard Brauer using modular representation theory playedan important role in early progress towards theclassification of finite simple groups, especially for simple groups whose characterization was not amenable to purely group-theoretic methods because their Sylow 2 subgroups were too small in an appropriate sense. Also, a general result on embedding of elements of order in finite groups called the Z* theorem, proved by George Glauberman using the theory developed by Brauer, was particularly useful in the classification program.If the characteristic of K does not divide the order of the group, G, then modular representations are completely reducible, as with ordinary(characteristic 0) representations, by virtue of Maschke's theorem. The proof of Maschke's theorem relies on being able to divide by the group order, which is not meaningful when the order of G is divisible by the characteristic of K. In that case, representations need not becompletely reducible, unlike the ordinary (and the coprime characteristic) case. Much of the discussion below implicitly assumesthat the field K is sufficiently large (for example, K algebraically closed suffices), otherwise some statements need refinement.".
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- Modular_representation_theory wikiPageWikiLink Category:Finite_fields.
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- Modular_representation_theory wikiPageWikiLink Category:Representation_theory_of_finite_groups.
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- Modular_representation_theory wikiPageWikiLink Maschkes_theorem.
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- Modular_representation_theory wikiPageWikiLink Richard_Brauer.
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- Modular_representation_theory wikiPageWikiLink Sylow.
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- Modular_representation_theory wikiPageWikiLink Trivial_module.
- Modular_representation_theory wikiPageWikiLink Z*_theorem.
- Modular_representation_theory wikiPageWikiLinkText "Brauer character".
- Modular_representation_theory wikiPageWikiLinkText "Brauer characters".
- Modular_representation_theory wikiPageWikiLinkText "Modular representation theory".
- Modular_representation_theory wikiPageWikiLinkText "Modular representation theory#Brauer characters".
- Modular_representation_theory wikiPageWikiLinkText "block".
- Modular_representation_theory wikiPageWikiLinkText "blocks".
- Modular_representation_theory wikiPageWikiLinkText "defect group".
- Modular_representation_theory wikiPageWikiLinkText "modular characters".
- Modular_representation_theory wikiPageWikiLinkText "modular representation theory".
- Modular_representation_theory wikiPageWikiLinkText "modular representation".
- Modular_representation_theory wikiPageWikiLinkText "modular representations".
- Modular_representation_theory wikiPageWikiLinkText "positive characteristic case".
- Modular_representation_theory wikiPageWikiLinkText "principal block".
- Modular_representation_theory wikiPageWikiLinkText "representation".
- Modular_representation_theory hasPhotoCollection Modular_representation_theory.
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- Modular_representation_theory subject Category:Finite_fields.
- Modular_representation_theory subject Category:Module_theory.
- Modular_representation_theory subject Category:Representation_theory_of_finite_groups.
- Modular_representation_theory hypernym Branch.
- Modular_representation_theory type Group.
- Modular_representation_theory type Organisation.
- Modular_representation_theory type Field.
- Modular_representation_theory type Group.