Ivan Shishkin, Birch Grove

Lie group

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Revision 817

8/1/2026, 7:06:47 PM · Sequoia

Concept edited

Recorded titleLie group
Recorded typeDefinition
Compare with revision 6384 changed lines
1A Lie group is [[Smooth manifold|smooth manifold]] that is also a [[Group|group]], such that the group operations
1A Lie group $G$ is [[Smooth manifold|smooth manifold]] that is also a [[Group|group]], such that the functions
2$$(g,h)\mapsto gh,\quad g\mapsto g^{-1}$$
2$$(g,h)\in G^2\mapsto gh,\quad g\in G\mapsto g^{-1}$$
3are [[Smooth map|smooth maps]].

Revision 638

7/27/2026, 8:50:43 AM · Ancient Tree

Concept edited

Compare with revision 6372 changed lines
1A Lie group is [[Smooth manifold|smooth manifold]] that is also a [[Group|group]], such that the group operations
2$$(g,h)\mapsto gh,\quad g\mapsto g^{-1}$$
3are [[smooth maps|smooth maps]].
3are [[Smooth map|smooth maps]].

Revision 637

7/27/2026, 8:50:23 AM · Ancient Tree

Concept created

A Lie group is [[Smooth manifold|smooth manifold]] that is also a [[Group|group]], such that the group operations
$$(g,h)\mapsto gh,\quad g\mapsto g^{-1}$$
are [[smooth maps|smooth maps]].