∞-Lie theory (higher geometry)
generalized smooth space
smooth manifold
diffeological space
Frölicher space
smooth topos
smooth ∞-groupoid, concrete smooth ∞-groupoid
synthetic differential ∞-groupoid
∞-groupoid
groupoid
2-groupoid
strict ∞-groupoid
∞-group
Lie theory
Lie integration, Lie differentiation
Lie's three theorems
Lie theory for stacky Lie groupoids
∞-Lie groupoid
strict ∞-Lie groupoid
Lie groupoid
differentiable stack
orbifold
∞-Lie group
Lie group
Lie 2-group
∞-Lie algebroid
Lie ∞-algebroid representation
L-∞-algebra
model structure for L-∞ algebras: on dg-Lie algebras, on dg-coalgebras, on simplicial Lie algebras
Lie algebra
Lie 2-algebra
strict Lie 2-algebra
differential crossed module
Lie 3-algebra
dg-Lie algebra, simplicial Lie algebra
super L-∞ algebra
Lie algebra cohomology
Chevalley-Eilenberg algebra
Weil algebra
invariant polynomial
nonabelian Lie algebra cohomology
Atiyah Lie groupoid
fundamental ∞-groupoid
path groupoid
path n-groupoid
smooth principal ∞-bundle
orthogonal group
special orthogonal group
spin group
string 2-group
fivebrane 6-group
unitary group
circle Lie n-group
tangent Lie algebroid
action Lie algebroid
Atiyah Lie algebroid
symplectic Lie n-algebroid
symplectic manifold
Poisson Lie algebroid
Courant Lie algebroid
general linear Lie algebra
orthogonal Lie algebra, special orthogonal Lie algebra
endomorphism L-∞ algebra
automorphism ∞-Lie algebra
string Lie 2-algebra
fivebrane Lie 6-algebra
supergravity Lie 3-algebra
supergravity Lie 6-algebra
line Lie n-algebra
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A matrix Lie group is a Lie group that is canonically a matrix group, hence a subgroup of the general linear group GL nGL_n on ℝ n\mathbb{R}^n or ℂ n\mathbb{C}^n.
See also matrix Lie algebra.