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Projective representation

In the field of representation theory in mathematics, a projective representation of a group G on a vector space V over a field F is a group homomorphism from G to the projective linear group P G L ( V ) = G L ( V ) / F ∗ , {\displaystyle \mathrm {PGL} (V)=\mathrm {GL} (V)/F^{*},} where GL(V) is the general linear group of invertible linear…

Projective representations of Lie groups, Linear representations and projective representations & Overview

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Projective representations of Lie groups

Lie groupsCovering groupsUnitary representationSU(2)Study of representations of SU(2)
34 related topics

Linear representations and projective representations

Group representationDiagonal matricesObstructionGroup cohomologyCentral extension
14 related topics

Overview

Representation theoryMathematicsGroupVector spaceField
13 related topics

First example: Finite abelian groups

Trivial representationAlgebraically closed fieldRoot of unity
3 related topics

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Overview

Linear representations and projective representations

First example: Finite abelian groups

Discrete Fourier transform

Projective representations of Lie groups

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Projective representation

Nodes73
Edges72
Triples105
Avg. degree1.97
Density0.027397
Components1

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Projective representation

Top relations

related to References · 36
Projective representation → An Elementary Introduction, Annals, Bargmann, Bargmann's, Bibcode, Brian, Cambridge University Press, Crelle's Journal, Darstellung, Graduate Texts, Gruppe, ISBN, JSTOR, Lie, Lie Algebras, Lie Groups, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, Mathematical Physics
related to Examples of covers, leading to projective representations · 18
Projective representation → An, Both, In, Mp, Möbius, Notable, Passing, Pin, Poincaré, R4, SL2, SO, Sp, Spin, SU, The, This, Wigner's
related to Projective representations of Lie groups · 15
Projective representation → GL, Group, In, Lie, Note, PGL, Pi, Schur's, Since, Specifically, Studying, Suppose, That, Then, Thus
related to Infinite-dimensional projective unitary representations: Bargmann's theorem · 11
Projective representation → Bargmann's, Examples, Lie, More, On, Poincaré, SL, The, Then, This, Wigner's
related to General cyclic group · 6
Projective representation → GL, Hence, Id, Now, Since, The
related to Projective representations of SO(3) · 6
Projective representation → According, By, SO, SU, Such, When
related to Discrete Fourier transform · 4
Projective representation → Consider, For, Fourier, The
related to Linear representations and projective representations · 4
Projective representation → GL, One, PGL, The
related to The group with 2 elements · 4
Projective representation → Consider, In, The, This
is a · 1
Projective representation → same as ρ

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Important terminology

displaystyle representation projective rho group sigma representations linear unitary mathbb operators ordinary tilde central gl scalar case extension mathrm lie

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Projective representationis asame as ρ0.90text
Projective representationrelated to Discrete Fourier transformThe0.60section
Projective representationrelated to Discrete Fourier transformFourier0.60section
Projective representationrelated to Discrete Fourier transformConsider0.60section
Projective representationrelated to Discrete Fourier transformFor0.60section
Projective representationrelated to Examples of covers, leading to projective representationsNotable0.60section
Projective representationrelated to Examples of covers, leading to projective representationsThe0.60section
Projective representationrelated to Examples of covers, leading to projective representationsSO0.60section
Projective representationrelated to Examples of covers, leading to projective representationsSpin0.60section
Projective representationrelated to Examples of covers, leading to projective representationsIn0.60section
Projective representationrelated to Examples of covers, leading to projective representationsSU0.60section
Projective representationrelated to Examples of covers, leading to projective representationsThis0.60section

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