|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:abbreviation
|
gptkb:SL(n,_F)
|
|
gptkbp:actsOn
|
vector spaces
|
|
gptkbp:centralTo
|
scalar matrices with n-th roots of unity
|
|
gptkbp:connectedTo
|
yes (over complex numbers)
|
|
gptkbp:consistsOf
|
n x n matrices with determinant 1
|
|
gptkbp:definedIn
|
gptkb:Field
|
|
gptkbp:defines
|
determinant = 1
|
|
gptkbp:dimensions
|
n^2 - 1
|
|
gptkbp:for_n=2
|
gptkb:SL(2,_F)
|
|
gptkbp:for_n=3
|
SL(3, F)
|
|
gptkbp:has_finite_analogues
|
yes
|
|
gptkbp:has_universal_cover
|
yes (for Lie group version)
|
|
gptkbp:hasProperty
|
preserves orientation
preserves volume
|
|
gptkbp:hasSubgroup
|
gptkb:general_linear_group
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Special linear group
|
|
gptkbp:importantFor
|
gptkb:algebraic_geometry
group theory
physics
representation theory
linear algebra
|
|
gptkbp:is_algebraic_group
|
yes
|
|
gptkbp:is_algebraic_group_over
|
any field
|
|
gptkbp:is_Chevalley_group
|
yes
|
|
gptkbp:is_classical_group
|
yes
|
|
gptkbp:is_finite
|
if F is finite
|
|
gptkbp:is_infinite
|
if F is infinite
|
|
gptkbp:is_Lie_group
|
yes
|
|
gptkbp:is_linear_algebraic_group
|
yes
|
|
gptkbp:is_matrix_group
|
yes
|
|
gptkbp:is_perfect_group
|
yes for n > 2
|
|
gptkbp:is_reductive
|
yes
|
|
gptkbp:is_simple_group
|
for n > 2 and F not too small
|
|
gptkbp:is_simple_Lie_group
|
for n > 2
|
|
gptkbp:isNonAbelian
|
for n > 1
|
|
gptkbp:isSemisimple
|
yes
|
|
gptkbp:Lie_algebra
|
special linear Lie algebra sl(n, F)
|
|
gptkbp:notation
|
gptkb:SL(n,_F)
|
|
gptkbp:order
|
depends on n and F
|
|
gptkbp:relatedTo
|
orthogonal group
projective special linear group
|
|
gptkbp:used_in
|
gptkb:topology
differential geometry
number theory
particle physics
quantum mechanics
theory of modular forms
|
|
gptkbp:bfsParent
|
gptkb:group_of_people
|
|
gptkbp:bfsLayer
|
4
|