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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Weights and roots
Weights and roots organize representations and structure relative to suitable commuting subalgebras.
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Lie algebras
A Lie algebra has a bilinear alternating bracket satisfying the Jacobi identity.
Tensor products of representations
Actions on factor spaces induce a compatible action on their tensor product.
Characters
A finite-dimensional representation's character assigns the trace of each represented element.
Complete reducibility
A representation is completely reducible when it is a direct sum of irreducible representations.
Group representations
A group representation is a homomorphism into invertible linear transformations.
Knowledge connections
- Lie algebras · Related · Map context
- Tensor products of representations · Related · Map context