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{{Group theory sidebar |Topological}}
== Gu Nanhai brow is wrinkled ==
{{Lie groups |Other}}
{{for|groups of actors involved in re-recording movie dialogue during post-production (commonly known in the entertainment industry as "loop groups")|Dubbing (filmmaking)}}


In [[mathematics]], a '''loop group''' is a [[Group (mathematics)|group]] of [[Loop (topology)|loops]] in a [[topological group]] ''G'' with multiplication defined pointwise. Specifically, let ''LG'' denote the [[Topological space|space]] of [[Continuous function (topology)|continuous maps]]<math>S^1 \to G</math> equipped with the [[compact-open topology]].  An element of <math>LG</math> is called a ''loop'' in G. Pointwise multiplication of such loops gives <math>LG</math> the structure of a topological group. The space <math>LG</math> is called the '''free loop group''' on <math>G</math>. A loop group is any [[subgroup]] of the free loop group <math>LG</math>.
Sea faint smile, Gang Yu once again to say something, the surrounding space, sudden severe fluctuations since a thrill of horror temperature, [http://www.nnyagdev.org/sitemap.xml http://www.nnyagdev.org/sitemap.xml] sailed from the surrounding diffuse open.<br><br>'Be careful!'<br><br>see this scene, Gu Nanhai brow is wrinkled, said.<br><br>course, no reminding, at the moment, Xiao go far people have filed a heart, looking more and more twisted [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-8.html カシオ レディース 電波ソーラー腕時計] around watchful eyes of space, this space [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-11.html カシオ 電波時計] is too strange fire demon, have to be cautious.<br><br>'roaring!'<br><br>With more distorted space to get later, a road crack suddenly emerged out of these cracks, like the waves of a Unit as 'milk' white 'color' flame, since which swept open, followed by, covered [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-2.html カシオの時計] with a road filled with 'milk' white 'color' flame figure, such as 'boom' like water from the storm surge out of the many cracks in the blink of an eye, the square outside the sky, who is to be the [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-10.html casio 腕時計 データバンク] flame
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An important example of a loop group is the group
== it seems you are very Yunshan fear ah ==
:<math>\Omega G \,</math>


of based loops on <math>G</math>. It is defined to be the kernel of the evaluation map
.<br><br>'Hey, you old dog Yunshan this hand it very ruthless [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-2.html casio 腕時計 デジタル] ah. Hell, [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-15.html カシオ ソーラー 腕時計] Gouji you still jump off the wall, the rabbit [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-4.html カシオ 電波ソーラー時計] is also anxious to bite you it was' forced 'After two days I was on cloud Arashiyama.'<br><br>finger on dark refers slight flick, 'medicine' that old figure is slowly wafting [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-13.html 時計 カシオ] illusory, he looked at Xiao Yan, said: 'battlefield Arashiyama in the cloud, [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-7.html カシオ 腕時計 gps] cloud-lan has the terrain, the disciples were also numerous In the mountains, there are more people this trend, hey, it seems you are very Yunshan fear ah, otherwise do not use so much thought. '<br><br>Xiao Yan nodded, cloud-lan many people, but also know how to punch battle, but that punch battle for power, he is personally experienced the year, the natural thing is to know that tyranny.<br><br>'you rhyme with those between clouds, Yunshan probably also know, and so he moves, there is a fear also angered and disturbed' mess 'the intent of your heart,' 'medicine' old Shen '
:<math>e_1: LG \to G</math>,
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and hence is a closed normal subgroup of <math>LG</math>.  (Here, <math>e_1</math> is the map that sends a loop to its value at <math>1</math>.)  Note that we may embed <math>G</math> into <math>LG</math> as the subgroup of constant loops.  Consequently, we arrive at a split exact sequence
== if re-Bushi Xiang ==
:<math>1\to \Omega G \to LG \to G\to 1</math>.


The space <math>LG</math> splits as a [[semi-direct product]],  
The two city in the horizon of two old reputation is not [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-7.html カシオ 腕時計 gps] weak, rapid footsteps mounted the pedal back, while the other hand young black robes that name, it was like a rock-solid, motionless.<br><br>'today than, blame, if re-Bushi Xiang, can [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-0.html カシオ 腕時計 バンド] not blame the next ruthless!'<br><br>Xiao Yan eyes looking at the two chill man, in the eyes of the intention to kill, reveals the slightest cold, today this thing is already going beyond his bottom line.<br><br>Xiao Yan out [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-9.html カシオ 腕時計 チタン] previously demonstrated the strength [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-8.html カシオ レディース 電波ソーラー腕時計] of the shock and awe, two old man is afraid to be Alert, but the hearts crying, this sister, 'milk', 'milk' run amok for so many years, finally hit the muzzle up, This kid may [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-5.html カシオ 腕時計 スタンダード] look young, but the strength is not extremely weak, and that the previous single-handedly, even family, is only very few of the few people able to cast out.<br><br>'the friend, the next is the home of the Romanian people, who previously collision your girl, Luo home
:<math>LG = \Omega G \rtimes G</math>.
相关的主题文章：
 
<ul>
We may also think of <math>\Omega G</math> as the [[loop space]] on <math>G</math>. From this point of view, <math>\Omega G</math> is an [[H-space|''H''-space]] with respect to concatenation of loops.  On the face of it, this seems to provide <math>\Omega G</math> with two very different product maps.  However, it can be shown that concatenation and pointwise multiplication are [[homotopy|homotopic]].  Thus, in terms of the homotopy theory of <math>\Omega G</math>, these maps are interchangeable.
 
 
  <li>[http://www.k9158.com/user/space.php?uid=23177&do=blog&id=47671 http://www.k9158.com/user/space.php?uid=23177&do=blog&id=47671]</li>
Loop groups were used to explain the phenomenon of [[Bäcklund transform]]s in [[soliton]] equations by [[Chuu-Lian Terng]] and [[Karen Uhlenbeck]].<ref>[http://www.ams.org/notices/200001/fea-terng.pdf Geometry of Solitons] by Chuu-Lian Terng and Karen Uhlenbeck</ref>
 
 
  <li>[http://nii.room.ne.jp/~zunchan/cgi-bin/sakura/cosme/petit.cgi http://nii.room.ne.jp/~zunchan/cgi-bin/sakura/cosme/petit.cgi]</li>
== Notes ==
 
{{reflist}}
  <li>[http://anxinyt.com/plus/feedback.php?aid=281 http://anxinyt.com/plus/feedback.php?aid=281]</li>
 
 
== References ==
</ul>
*{{citation |mr=0900587 |last=Pressley |first=Andrew |last2=Segal |first2=Graeme |title=Loop groups |series=Oxford Mathematical Monographs. Oxford Science Publications |publisher=The Clarendon Press, Oxford University Press, New York |year=1986 |isbn=0-19-853535-X |url=http://books.google.com/books?id=MbFBXyuxLKgC}}
 
== See also ==
*[[Loop space]]
*[[Loop algebra]]
*[[Quasigroup]]
 
[[Category:Topological groups]]
[[Category:Solitons]]

Revision as of 06:01, 20 February 2014

Gu Nanhai brow is wrinkled

Sea faint smile, Gang Yu once again to say something, the surrounding space, sudden severe fluctuations since a thrill of horror temperature, http://www.nnyagdev.org/sitemap.xml sailed from the surrounding diffuse open.

'Be careful!'

see this scene, Gu Nanhai brow is wrinkled, said.

course, no reminding, at the moment, Xiao go far people have filed a heart, looking more and more twisted カシオ レディース 電波ソーラー腕時計 around watchful eyes of space, this space カシオ 電波時計 is too strange fire demon, have to be cautious.

'roaring!'

With more distorted space to get later, a road crack suddenly emerged out of these cracks, like the waves of a Unit as 'milk' white 'color' flame, since which swept open, followed by, covered カシオの時計 with a road filled with 'milk' white 'color' flame figure, such as 'boom' like water from the storm surge out of the many cracks in the blink of an eye, the square outside the sky, who is to be the casio 腕時計 データバンク flame 相关的主题文章：

it seems you are very Yunshan fear ah

.

'Hey, you old dog Yunshan this hand it very ruthless casio 腕時計 デジタル ah. Hell, カシオ ソーラー 腕時計 Gouji you still jump off the wall, the rabbit カシオ 電波ソーラー時計 is also anxious to bite you it was' forced 'After two days I was on cloud Arashiyama.'

finger on dark refers slight flick, 'medicine' that old figure is slowly wafting 時計 カシオ illusory, he looked at Xiao Yan, said: 'battlefield Arashiyama in the cloud, カシオ 腕時計 gps cloud-lan has the terrain, the disciples were also numerous In the mountains, there are more people this trend, hey, it seems you are very Yunshan fear ah, otherwise do not use so much thought. '

Xiao Yan nodded, cloud-lan many people, but also know how to punch battle, but that punch battle for power, he is personally experienced the year, the natural thing is to know that tyranny.

'you rhyme with those between clouds, Yunshan probably also know, and so he moves, there is a fear also angered and disturbed' mess 'the intent of your heart,' 'medicine' old Shen ' 相关的主题文章：

if re-Bushi Xiang

The two city in the horizon of two old reputation is not カシオ 腕時計 gps weak, rapid footsteps mounted the pedal back, while the other hand young black robes that name, it was like a rock-solid, motionless.

'today than, blame, if re-Bushi Xiang, can カシオ 腕時計 バンド not blame the next ruthless!'

Xiao Yan eyes looking at the two chill man, in the eyes of the intention to kill, reveals the slightest cold, today this thing is already going beyond his bottom line.

Xiao Yan out カシオ 腕時計 チタン previously demonstrated the strength カシオ レディース 電波ソーラー腕時計 of the shock and awe, two old man is afraid to be Alert, but the hearts crying, this sister, 'milk', 'milk' run amok for so many years, finally hit the muzzle up, This kid may カシオ 腕時計 スタンダード look young, but the strength is not extremely weak, and that the previous single-handedly, even family, is only very few of the few people able to cast out.

'the friend, the next is the home of the Romanian people, who previously collision your girl, Luo home 相关的主题文章：

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