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).
Resources
[edit | edit source]- Topic:linear representations of finite groups
- Topic:Lie groups and Lie algebras
- Complex semi-simple Lie algebras and their representations
- Topic:Virasoro algebra
Offsite Learning Materials
[edit | edit source]Recommended Reading Material
[edit | edit source]- 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