Representation Theory
Explore linear actions; characters and decomposition; construction and lie theory. Concepts and connections are available independently of video coverage.
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Group representations
A group representation is a homomorphism into invertible linear transformations.
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Characters
A finite-dimensional representation's character assigns the trace of each represented element.
Group homomorphisms
A homomorphism preserves group multiplication; its kernel measures failure of injectivity.
Intertwining operators
An intertwiner is a linear map commuting with the represented group actions.
Invariant subspaces
An invariant subspace is preserved by every transformation in a representation.
Vector spaces
A vector space specifies addition and scalar multiplication satisfying the vector-space axioms over a chosen field.
Knowledge connections
- Invariant subspaces · Related · Map context
- Intertwining operators · Related · Map context
- Group homomorphisms · Related · Map context
- Characters · Related · Map context
- Group homomorphisms · Prerequisite · Map context
- Vector spaces · Prerequisite · Map context