Revision #1839 → #2350 · back to history
modifiedSymplectic group84643b591fc9
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| anchor.snippet | The symplectic group [MATH] consists of all | matrices preserving the symplectic form |
| provenance | ai | ai-moderated |
modifiedSimply connected Lie group2e7f71ccaeae
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| anchor.snippet | A Lie group [MATH] is said to be simply connected if every loop in | is said to be simply connected if every loop in |
| provenance | ai | ai-moderated |
modifiedLifting Lie algebra homomorphisms to simply connected groups572c722a63ff
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| anchor.snippet | Suppose [MATH] and [MATH] are Lie groups with Lie algebras | there is a unique Lie group homomorphism |
| provenance | ai | ai-moderated |
modifiedExponential map (matrix case)099fc3616837
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| anchor.snippet | The exponential map from the Lie algebra [MATH] of the general linear group [MATH] to [MATH] is defined by the matrix exponential | is defined by the matrix exponential , given by the usual power series |
| provenance | ai | ai-moderated |
modifiedLie subgroup8a5df4364aa6
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| anchor.snippet | A Lie subgroup [MATH] of a Lie group [MATH] is a Lie group that is a subset of | is an injective immersion and group homomorphism |
| provenance | ai | ai-moderated |
modifiedCartan's closed subgroup theoreme8123dfcfa0e
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| anchor.snippet | According to Cartan's theorem , a closed subgroup of [MATH] admits a unique smooth structure | admits a unique smooth structure which makes it an embedded Lie subgroup |
| provenance | ai | ai-moderated |
addedConnected abelian Lie group is a product of copies of R and the circle093cba6c44c6
addedProduct of two Lie groups is a Lie group3dda0c9b4a55
addedLie bracket of a connected Lie group is zero iff the group is abelian23ab6f34f4e8