Lie theory MOC

1-parameter group

A 1-parameter group is a continuous group homomorphism

where is a topological group. lie Often, we abuse terminology and conflate with .

Local 1-parameter group

A local 1-parameter group is a weakening akin to a local group.¹ We restrict to a flow domain for , and take

We require that and for all such that .

See also

• Flow on a manifold

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Footnotes

1. In fact, may be a local group. ↩