. . . . "1068615965"^^ . . . . . . . . . . . . . . . . . . . . . . . . . . . "6798"^^ . . . "55872661"^^ . . . . "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."@en . . . . . . . . . . . . . . . . . "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."@en . . . . . . . "Category of representations"@en . . . . . . . . . . . . .