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Two different Lie groups can have the same Lie algebra
Lie group-Lie algebra correspondence
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42
The most important example is perhaps
$SO(3)$
and
$SU(2)$
, both of which have the same
Lie algebra
, but are not isomorphic.
Table of contents
42
Every Lie algebra has a unique single corresponding simply connected Lie group
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Two different Lie groups can have the same Lie algebra
17
Universal covering group
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Every Lie algebra has a unique single corresponding simply connected Lie group
6
Every Lie group that has a given Lie algebra is the image of an homomorphism from the universal cover group
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Two different Lie groups can have the same Lie algebra
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Ancestors
Lie group-Lie algebra correspondence
Lie algebra
Lie group
Differential geometry
Geometry
Mathematics
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