Representation Theory
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Representation theory is a branch of mathematics that studies abstract algebra|abstract algebraic structures by representing their element (set theory)|elements as linear transformations of vector spaces, and studiesModule (mathematics)|modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrix (mathematics)|matrices and the algebraic operations in terms of matrix addition and matrix multiplication. The algebraic objects amenable to such a description include group (mathematics)|groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the group representation|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. Representation theory is a powerful tool because it reduces problems in abstract algebra to problems in linear...
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Lie Algebra    
Lower Bound    
Finite Group    
Indexation    
Lie Group    
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