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gptkbp:instanceOf
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gptkb:group_of_people
|
|
gptkbp:application
|
gptkb:algebraic_geometry
physics
representation theory
linear algebra
|
|
gptkbp:centralTo
|
scalar matrices with n-th roots of unity
|
|
gptkbp:definedIn
|
group of n x n matrices with determinant 1
|
|
gptkbp:dimensions
|
n^2 - 1
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|
gptkbp:field
|
arbitrary field
|
|
gptkbp:firstAppearance
|
19th century
|
|
gptkbp:fullName
|
special linear group of degree n
|
|
gptkbp:generation
|
elementary matrices
|
|
gptkbp:hasSubgroup
|
gptkb:GL(n)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(n)
|
|
gptkbp:namedFor
|
mathematicians in group theory
|
|
gptkbp:notation
|
gptkb:SL(n,_F)
|
|
gptkbp:order
|
finite when F is finite field
product_{k=0}^{n-1}(q^n - q^k) / (q-1)
|
|
gptkbp:property
|
Lie group when F = R or C
simple group for n > 2 and F algebraically closed
|
|
gptkbp:relatedTo
|
gptkb:orthogonal_group_O(n)
gptkb:unitary_group_U(n)
general linear group GL(n)
projective special linear group PSL(n)
|
|
gptkbp:type
|
gptkb:algebraic_geometry
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:usedIn
|
gptkb:geometry
number theory
study of symmetries
|
|
gptkbp:bfsParent
|
gptkb:SL(2)
gptkb:special_linear_group_SL(n)
gptkb:GL(n)
|
|
gptkbp:bfsLayer
|
7
|