e/Representation theory

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has glosseng: Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and the algebraic operations in terms of matrix addition and matrix multiplication. The algebraic objects amenable to such a description include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in which elements of a group are represented by invertible matrices in such a way that the group operation is matrix multiplication.
lexicalizationeng: Representation theory
instance ofe/Topological group
Meaning
Bosnian
lexicalizationbos: Teorija reprezentacije
Danish
has glossdan: Repræsentationsteori er en gren af matematikken, der studerer abstrakte algebraiske strukturer ved at repræsentere deres elementer som lineære transformationer af vektorrum. En repræsentation vil essentielt gøre abstrakte algebraiske objekter mere konkrete ved at beskrive elementerne som matricer og de algebraiske operationer i termer af matrixaddition og matrixmultiplikation. De algebraiske objekter, der lader sig repræsentere på denne vis, omfatter grupper, associative algebraer og Liealgebraer. Den mest omfattende teori (og den historisk første) er repræsentationsteorien for grupper, hvor gruppeelementerne er repræsenteret af invertible matricer, således at gruppeoperationen svarer til matrixmultiplikation.
lexicalizationdan: repræsentationsteori
German
lexicalizationdeu: Darstellungstheorie
Esperanto
lexicalizationepo: Prezenta teorio
French
lexicalizationfra: Théorie des représentations
Dutch
has glossnld: Representatietheorie is een tak van de wiskunde, die abstracte algebraïsche structuren bestudeert door hun elementen te representeren als lineaire transformaties van vectorruimten.
lexicalizationnld: representatietheorie
Portuguese
has glosspor: Teoria da representação é um campo da matemática que estuda estruturas algébricas abstratas pela representação de seus elementos como transformações lineares de espaços vetoriais.
lexicalizationpor: Teoria da representação
Russian
has glossrus: Раздел математики, который изучает представления групп, называется теорией представлений групп.
lexicalizationrus: Теория представлений
Chinese
has glosszho: 表示論是數學中抽象代數的一支。旨在將代數結構中的元素「表示」成向量空間上的線性變換,藉以研究結構的性質。
lexicalizationzho: 表示论

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