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Key terms:
lie group
lie algebra
subgroup
abelian
mathfrak
banach
solvable
nilpotent
symmetries
vector fields
homomorphism
isomorphic
lie bracket
semisimple
connected lie group
exponential map
invertible
tangent space
symplectic
simple lie groups
diffeomorphism
infinite dimensional
sophus lie
abelian lie
solvable group
smooth manifold
banach analytic
galois theory
abelian group
differential equations
semisimple lie
continuous symmetry
nilpotent group
normal subgroup
closed subgroup
homomorphism between
banach manifold
upper triangular
symplectic group
semisimple group
finite dimensional lie
differentiable manifold
connected subgroup
invertible matrices
simply connected lie group
left invariant vector fields
dimensional lie groups
matrices of determinant
lie group is isomorphic
every finite dimensional
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