Representations of groups

E503510

area of representation theory branch of mathematics topic in abstract algebra

Representations of groups is a branch of mathematics that studies how abstract groups can act as linear transformations on vector spaces, typically via homomorphisms into groups of matrices.

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Observed surface forms (2)

Surface form	Occurrences
Lie group representation	1
Lorentz group representations	1

Statements (50)

Predicate	Object
instanceOf	area of representation theory ⓘ branch of mathematics ⓘ topic in abstract algebra ⓘ
appliesTo	Lie groups NERFINISHED ⓘ abelian groups ⓘ compact groups ⓘ finite groups ⓘ locally compact groups ⓘ non-abelian groups ⓘ
formalizedAs	functors from a group to the category of vector spaces ⓘ
goal	classify representations up to equivalence ⓘ decompose representations into irreducible components ⓘ
hasSubfield	modular representation theory ⓘ p-adic group representations ⓘ representation theory of Lie groups ⓘ representation theory of finite groups ⓘ unitary representation theory ⓘ
historicallyDevelopedBy	Ferdinand Frobenius NERFINISHED ⓘ Hermann Weyl NERFINISHED ⓘ Issai Schur NERFINISHED ⓘ
relatedTo	Fourier analysis on groups ⓘ category theory ⓘ harmonic analysis ⓘ invariant theory ⓘ number theory ⓘ particle physics ⓘ quantum mechanics NERFINISHED ⓘ symmetry ⓘ
studies	group actions by linear transformations on vector spaces ⓘ group homomorphisms into general linear groups ⓘ group homomorphisms into matrix groups ⓘ
usesConcept	Maschke's theorem NERFINISHED ⓘ Schur's lemma NERFINISHED ⓘ character of a representation ⓘ complete reducibility ⓘ general linear group NERFINISHED ⓘ group ⓘ group algebra ⓘ group homomorphism ⓘ induced representation ⓘ invariant subspace ⓘ irreducible representation ⓘ linear transformation ⓘ matrix representation ⓘ module over a ring ⓘ reducible representation ⓘ regular representation ⓘ restriction of representations ⓘ unitary representation ⓘ vector space ⓘ

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

The Classical Groups: Their Invariants and Representations → libraryOfCongressSubject → Representations of groups ⓘ

Lie algebra representation → relatedTo → Representations of groups ⓘ

this entity surface form: Lie group representation

spin–statistics theorem → isRelatedTo → Representations of groups ⓘ

this entity surface form: Lorentz group representations