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gptkbp:instanceOf
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gptkb:group_of_people
gptkb:Lie_group
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gptkbp:application
|
gptkb:algebraic_geometry
gptkb:theoretical_physics
differential geometry
representation theory
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gptkbp:centralTo
|
cyclic group of order 3
{λI | λ^3=1, λ∈ℂ}
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|
gptkbp:containsElement
|
3x3 complex matrices with determinant 1
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|
gptkbp:dimensions
|
8
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|
gptkbp:field
|
ℂ
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|
gptkbp:fullName
|
Special Linear Group of degree 3 over the complex numbers
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|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(3,ℂ)
|
|
gptkbp:identityElement
|
3x3 identity matrix
|
|
gptkbp:isQuotientOf
|
PSL(3,ℂ)
|
|
gptkbp:Lie_algebra
|
sl(3,ℂ)
|
|
gptkbp:matrixCondition
|
determinant equals 1
|
|
gptkbp:maximalCompactSubgroup
|
gptkb:SU(3)
|
|
gptkbp:notation
|
gptkb:SL(3,C)
SL_3(ℂ)
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|
gptkbp:rank
|
2
|
|
gptkbp:relatedGroup
|
gptkb:semisimple_Lie_group
gptkb:Lie_group
non-compact Lie group
connected Lie group
|
|
gptkbp:relatedTo
|
gptkb:special_unitary_group_SU(3)
general linear group GL(3,ℂ)
projective linear group PSL(3,ℂ)
special linear group SL(n,ℂ)
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|
gptkbp:structure
|
gptkb:Lie_group
algebraic group over ℂ
|
|
gptkbp:type
|
gptkb:A2
|
|
gptkbp:universalCover
|
itself
|
|
gptkbp:Weyl_group
|
gptkb:symmetric_group_S_3
|
|
gptkbp:bfsParent
|
gptkb:SL(3,C)
gptkb:SL(3,ℝ)
|
|
gptkbp:bfsLayer
|
7
|