Proof of the associated Lie algebra is isomorphic to $T_e(G)$ [duplicate]
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This question already has an answer here:
Lie algebra and tangent space at the identity are isomorphic
1 answer
I´m looking for a book with the proof of the result that says the associated Lie algebra of a Lie group $G$, let be $G_{Lie}$, is isomorphic to the tangent space $T_e(G)$, where $e in G$ is the neutral element.
Let me said the chapter or theorem, not only the book, please.
Thank you all
differential-geometry
asked Dec 13 '18 at 19:50
LH8LH8
1368
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marked as duplicate by Dietrich Burde, Saad, Lord Shark the Unknown, Jyrki Lahtonen, BigbearZzz Dec 14 '18 at 5:34
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
$begingroup$
This question already has an answer here:
Lie algebra and tangent space at the identity are isomorphic
1 answer
I´m looking for a book with the proof of the result that says the associated Lie algebra of a Lie group $G$, let be $G_{Lie}$, is isomorphic to the tangent space $T_e(G)$, where $e in G$ is the neutral element.
Let me said the chapter or theorem, not only the book, please.
Thank you all
differential-geometry
asked Dec 13 '18 at 19:50
LH8LH8
1368
$endgroup$
marked as duplicate by Dietrich Burde, Saad, Lord Shark the Unknown, Jyrki Lahtonen, BigbearZzz Dec 14 '18 at 5:34
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
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It's Chapter $21$, pages 81-84.
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– Dietrich Burde
Dec 13 '18 at 19:52
1
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I thought that the lie algebra was defined to be the tangent space at the identity (with Lie bracket defined by bracket of vector fields, where we extend individual vectors to locally nice vector fields first). That would certainly make the proof easy. :)
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– John Hughes
Dec 13 '18 at 19:56
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Ah...I suppose that makes sense.
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– John Hughes
Dec 13 '18 at 20:14
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I asked a concrete book, not just notes. I asked a reference book. The link is only a doubt.
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– LH8
Dec 13 '18 at 21:57
add a comment |
$begingroup$
This question already has an answer here:
Lie algebra and tangent space at the identity are isomorphic
1 answer
I´m looking for a book with the proof of the result that says the associated Lie algebra of a Lie group $G$, let be $G_{Lie}$, is isomorphic to the tangent space $T_e(G)$, where $e in G$ is the neutral element.
Let me said the chapter or theorem, not only the book, please.
Thank you all
differential-geometry
asked Dec 13 '18 at 19:50
LH8LH8
1368
$endgroup$
This question already has an answer here:
Lie algebra and tangent space at the identity are isomorphic
1 answer
I´m looking for a book with the proof of the result that says the associated Lie algebra of a Lie group $G$, let be $G_{Lie}$, is isomorphic to the tangent space $T_e(G)$, where $e in G$ is the neutral element.
Let me said the chapter or theorem, not only the book, please.
Thank you all
This question already has an answer here:
Lie algebra and tangent space at the identity are isomorphic
1 answer
differential-geometry
differential-geometry
asked Dec 13 '18 at 19:50
LH8LH8
1368
asked Dec 13 '18 at 19:50
LH8LH8
1368
asked Dec 13 '18 at 19:50
LH8LH8
1368
asked Dec 13 '18 at 19:50
LH8LH8
1368
asked Dec 13 '18 at 19:50
LH8LH8
1368
1368
marked as duplicate by Dietrich Burde, Saad, Lord Shark the Unknown, Jyrki Lahtonen, BigbearZzz Dec 14 '18 at 5:34
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Dietrich Burde, Saad, Lord Shark the Unknown, Jyrki Lahtonen, BigbearZzz Dec 14 '18 at 5:34
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
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It's Chapter $21$, pages 81-84.
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– Dietrich Burde
Dec 13 '18 at 19:52
1
$begingroup$
I thought that the lie algebra was defined to be the tangent space at the identity (with Lie bracket defined by bracket of vector fields, where we extend individual vectors to locally nice vector fields first). That would certainly make the proof easy. :)
$endgroup$
– John Hughes
Dec 13 '18 at 19:56
$begingroup$
Ah...I suppose that makes sense.
$endgroup$
– John Hughes
Dec 13 '18 at 20:14
$begingroup$
I asked a concrete book, not just notes. I asked a reference book. The link is only a doubt.
$endgroup$
– LH8
Dec 13 '18 at 21:57
add a comment |
$begingroup$
It's Chapter $21$, pages 81-84.
$endgroup$
– Dietrich Burde
Dec 13 '18 at 19:52
1
$begingroup$
I thought that the lie algebra was defined to be the tangent space at the identity (with Lie bracket defined by bracket of vector fields, where we extend individual vectors to locally nice vector fields first). That would certainly make the proof easy. :)
$endgroup$
– John Hughes
Dec 13 '18 at 19:56
$begingroup$
Ah...I suppose that makes sense.
$endgroup$
– John Hughes
Dec 13 '18 at 20:14
$begingroup$
I asked a concrete book, not just notes. I asked a reference book. The link is only a doubt.
$endgroup$
– LH8
Dec 13 '18 at 21:57
$begingroup$
It's Chapter $21$, pages 81-84.
$endgroup$
– Dietrich Burde
Dec 13 '18 at 19:52
$begingroup$
It's Chapter $21$, pages 81-84.
$endgroup$
– Dietrich Burde
Dec 13 '18 at 19:52
1
1
$begingroup$
I thought that the lie algebra was defined to be the tangent space at the identity (with Lie bracket defined by bracket of vector fields, where we extend individual vectors to locally nice vector fields first). That would certainly make the proof easy. :)
$endgroup$
– John Hughes
Dec 13 '18 at 19:56
$begingroup$
I thought that the lie algebra was defined to be the tangent space at the identity (with Lie bracket defined by bracket of vector fields, where we extend individual vectors to locally nice vector fields first). That would certainly make the proof easy. :)
$endgroup$
– John Hughes
Dec 13 '18 at 19:56
$begingroup$
Ah...I suppose that makes sense.
$endgroup$
– John Hughes
Dec 13 '18 at 20:14
$begingroup$
Ah...I suppose that makes sense.
$endgroup$
– John Hughes
Dec 13 '18 at 20:14
$begingroup$
I asked a concrete book, not just notes. I asked a reference book. The link is only a doubt.
$endgroup$
– LH8
Dec 13 '18 at 21:57
$begingroup$
I asked a concrete book, not just notes. I asked a reference book. The link is only a doubt.
$endgroup$
– LH8
Dec 13 '18 at 21:57
add a comment |
1 Answer
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Look at Introduction to Smooth Manifolds, 2nd edition by John Lee (great book). This is theorem 8.37, page 191.
answered Dec 14 '18 at 2:22
positrón0802positrón0802
4,468520
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add a comment |
1 Answer
1
active
oldest
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1 Answer
1
active
oldest
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active
oldest
votes
active
oldest
votes
$begingroup$
Look at Introduction to Smooth Manifolds, 2nd edition by John Lee (great book). This is theorem 8.37, page 191.
answered Dec 14 '18 at 2:22
positrón0802positrón0802
4,468520
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add a comment |
$begingroup$
Look at Introduction to Smooth Manifolds, 2nd edition by John Lee (great book). This is theorem 8.37, page 191.
answered Dec 14 '18 at 2:22
positrón0802positrón0802
4,468520
$endgroup$
add a comment |
$begingroup$
Look at Introduction to Smooth Manifolds, 2nd edition by John Lee (great book). This is theorem 8.37, page 191.
answered Dec 14 '18 at 2:22
positrón0802positrón0802
4,468520
$endgroup$
Look at Introduction to Smooth Manifolds, 2nd edition by John Lee (great book). This is theorem 8.37, page 191.
answered Dec 14 '18 at 2:22
positrón0802positrón0802
4,468520
answered Dec 14 '18 at 2:22
positrón0802positrón0802
4,468520
answered Dec 14 '18 at 2:22
positrón0802positrón0802
4,468520
answered Dec 14 '18 at 2:22
positrón0802positrón0802
4,468520
4,468520
add a comment |
add a comment |
$begingroup$
It's Chapter $21$, pages 81-84.
$endgroup$
– Dietrich Burde
Dec 13 '18 at 19:52
1
$begingroup$
I thought that the lie algebra was defined to be the tangent space at the identity (with Lie bracket defined by bracket of vector fields, where we extend individual vectors to locally nice vector fields first). That would certainly make the proof easy. :)
$endgroup$
– John Hughes
Dec 13 '18 at 19:56
$begingroup$
Ah...I suppose that makes sense.
$endgroup$
– John Hughes
Dec 13 '18 at 20:14
$begingroup$
I asked a concrete book, not just notes. I asked a reference book. The link is only a doubt.
$endgroup$
– LH8
Dec 13 '18 at 21:57