# Algebraic structures/Representation theory

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**Representation theory** is the study of symmetries. We study ways to represent abstract algebraic structures (groups, algebras, Lie algebras, etc) as linear transformations (e.g. matrices). Representation theory serves, and is enriched by, Algebra, Analysis, Geometry, Category Theory, Combinatorics, Number Theory and Theoretical Physics (where it is called *group theory*).

## Resources

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edit- J.-P. Serre:
*Linear Representations of Finite Groups* - J.-P. Serre:
*Complex Semi-simple Lie Algebras* - Fulton and Harris:
*Representation theory. A first course* - Knapp