Algebraic structures/Representation theory

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).

• Topic:linear representations of finite groups
• Topic:Lie groups and Lie algebras
• Complex semi-simple Lie algebras and their representations
• Topic:Virasoro algebra

• http://www.ams.org/online_bks/online_subject.html

• 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