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Two different Lie groups can have the same Lie algebra

The most important example is perhaps

SO (3)

and

S U (2)

, both of which have the same Lie algebra, but are not isomorphic.

Table of contents 42 3
- Every Lie algebra has a unique single corresponding simply connected Lie group Two different Lie groups can have the same Lie algebra 23 1
  - Universal covering group 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 Two different Lie groups can have the same Lie algebra

 Ancestors (8)