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Statements

Subject Item
dbr:Category_of_representations
rdf:type
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Category of representations
rdfs:comment
In representation theory, the category of representations of some algebraic structure A has the representations of A as objects and equivariant maps as morphisms between them. One of the basic thrusts of representation theory is to understand the conditions under which this category is semisimple; i.e., whether an object decomposes into simple objects (see Maschke's theorem for the case of finite groups). The Grothendieck ring of the category of finite-dimensional representations of a group G is called the representation ring of G.
rdfs:seeAlso
dbr:The_convolution_algebra dbr:Representation_theory_of_finite_groups dbr:Modules dbr:Equivariant_map
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dbc:Representation_theory dbc:Category_theory
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55872661
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1068615965
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dbo:abstract
In representation theory, the category of representations of some algebraic structure A has the representations of A as objects and equivariant maps as morphisms between them. One of the basic thrusts of representation theory is to understand the conditions under which this category is semisimple; i.e., whether an object decomposes into simple objects (see Maschke's theorem for the case of finite groups). The Tannakian formalism gives conditions under which a group G may be recovered from the category of representations of it together with the forgetful functor to the category of vector spaces. The Grothendieck ring of the category of finite-dimensional representations of a group G is called the representation ring of G.
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wikipedia-en:Category_of_representations?oldid=1068615965&ns=0
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wikipedia-en:Category_of_representations