|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
real n-dimensional vector space
|
|
gptkbp:centralTo
|
{I, -I} for n even; {I} for n odd
|
|
gptkbp:compact
|
true (for n > 1)
|
|
gptkbp:contains
|
gptkb:SO(n)
|
|
gptkbp:definedIn
|
the group of n x n real matrices with determinant 1
|
|
gptkbp:determinant
|
1
|
|
gptkbp:dimensions
|
n^2 - 1
|
|
gptkbp:field
|
real numbers
|
|
gptkbp:fullName
|
Special Linear Group of degree n over the real numbers
|
|
gptkbp:hasConnection
|
true
false (for n > 1)
|
|
gptkbp:hasSubgroup
|
gptkb:GL(n,R)
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true (for n > 1)
|
|
gptkbp:isSemisimple
|
true (for n > 1)
|
|
gptkbp:isSimple
|
true (for n > 2)
|
|
gptkbp:isTopologically
|
non-compact, connected Lie group
|
|
gptkbp:Lie_algebra
|
gptkb:sl(n,R)
|
|
gptkbp:notation
|
SL(n,ℝ)
|
|
gptkbp:realForm
|
gptkb:SL(n,C)
|
|
gptkbp:universalCover
|
true
|
|
gptkbp:usedIn
|
gptkb:partial_differential_equations
gptkb:Lie_theory
gptkb:algebraic_geometry
gptkb:general_relativity
gptkb:geometry
gptkb:special_relativity
gptkb:topology
coding theory
control theory
cryptography
differential geometry
dynamical systems
ergodic theory
group theory
mathematical physics
modular forms
number theory
physics
quantum mechanics
representation theory
algebraic groups
automorphic forms
symplectic geometry
|
|
gptkbp:bfsParent
|
gptkb:special_linear_group_SL(n,R)
|
|
gptkbp:bfsLayer
|
8
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(n,R)
|