Abstract Algebra
Explore groups and symmetry; rings and fields; extensions and actions. Concepts and connections are available independently of video coverage.
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Group homomorphisms
A homomorphism preserves group multiplication; its kernel measures failure of injectivity.
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Bijections
A bijection is both injective and surjective and has a two-sided inverse.
Cosets and Lagrange's theorem
Cosets partition a finite group, so a subgroup's order divides the group's order.
Group representations
A group representation is a homomorphism into invertible linear transformations.
Quotient groups
Cosets of a normal subgroup inherit a well-defined group operation.
Tensor products of representations
Actions on factor spaces induce a compatible action on their tensor product.
Knowledge connections
- Cosets and Lagrange's theorem · Related · Map context
- Quotient groups · Related · Map context
- Bijections · Prerequisite · Map context
- Vector spaces · Related · Map context
- Group representations · Related · Map context
- Tensor products of representations · Related · Map context
- Group representations · Next concept · Map context
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Representation Theory
Explore linear actions; characters and decomposition; construction and lie theory. Concepts and connections are available independently of video coverage.