en>DavidCary: /* See also */ other related articles

2014-12-26T21:09:53Z

en>NickPenguin: no consensus to merge

2014-03-01T20:13:58Z

no consensus to merge

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	~~In geometry, a '''complex Lie group'''~~ is a ~~complex~~-~~analytic manifold that is also a group in such~~ a ~~way <math>G \times G \to G~~, (x, ~~y) \mapsto x y^{~~-1}<~~/math~~> ~~is holomorphic. Basic examples are~~ <~~math~~>~~\operatorname{GL}_n(\mathbb{C})~~<~~/math~~>, the ~~[[general linear group]]s over~~ the ~~[[complex number]]s~~. ~~A connected compact complex Lie group is precisely~~ a ~~[[complex torus]]~~. ~~A complex [[semisimple Lie group]] is an [[algebraic group]]~~.<~~!--A corollay of this is that~~ a ~~connected real semisimple Lie group is a covering of~~ an ~~algebraic group~~. ~~-->~~		It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>If you have any concerns concerning where and ways to use [http://www.youtube.com/watch?v=90z1mmiwNS8 dentist DC], you can contact us at our own web-site.

	~~== Examples ==~~
	*A finite-dimensional vector space over the ~~complex numbers~~ (in ~~particular, complex Lie algebra~~) ~~is a complex Lie group~~ in ~~an obvious way~~.
	*A ~~connected compact complex Lie group ''~~A~~'' of dimension ''g'' is of the form~~ <~~math~~>~~\mathbb{C}^g/L~~<~~/math~~> ~~where ''L'' is a discrete subgroup~~. ~~Indeed, its Lie algebra <math>\mathfrak{a}</math> can~~ be ~~shown~~ to ~~be abelian~~ and ~~then <math>\operatorname{exp}: \mathfrak{a} \to A</math> is a [[surjection\|surjective]] [[morphism]]~~ of ~~complex Lie groups~~, ~~showing ''A'' is~~ of the ~~form described~~.
	* <~~math~~>~~\mathbb{C} \to \mathbb{C}^, z \mapsto e^z~~<~~/math~~> is ~~an example of~~ a ~~morphism~~ of ~~complex Lie groups that~~ does not ~~come from~~ a ~~morphism of algebraic groups~~. ~~Since~~ <~~math~~>~~\mathbb{C}^ = \operatorname{GL}_1(\mathbb{C})~~<~~/math~~>~~, this is also an example of~~ a ~~representation of~~ a ~~complex Lie group that is not algebraic~~.
	* Let ''X'' be a compact complex manifold. ~~Then~~, ~~as in~~ the ~~real case,~~ <~~math~~>~~\operatorname{Aut}(X)~~<~~/math~~> is a ~~complex Lie group whose Lie algebra is~~ <~~math~~>~~\Gamma(X, TX)~~<~~/math~~>.
	* Let ''K'' be a ~~connected [[compact Lie group]]~~. ~~Then there exists a unique connected complex Lie group ''G'' such that (i)~~ <~~math~~>~~\operatorname{Lie} (G) = \operatorname{Lie} (K) \otimes_{\mathbb{R}} \mathbb{C}~~<~~/math~~> (ii) ~~''K''~~ is a ~~maximal compact subgroup~~ of ~~''G''~~. ~~It is called~~ the ~~[[complexification (Lie group)\|complexification]]~~ of ~~''K''~~. ~~For example,~~ <~~math~~>~~\operatorname{GL}_n(\mathbb{C})~~<~~/math~~> ~~is the complexification of the [[unitary group]].~~ If ~~''K'' is acting on a compact kähler manifold ''X'', then the action of ''K'' extends~~ to ~~that of ''G''.{{fact\|date=April 2013}}~~

	~~== References ==~~
	*{{citation
	~~\| last = Lee \| first = Dong Hoon~~
	~~\| isbn = 1-58488-261-1~~
	~~\| mr = 1887930~~
	~~\| publisher = Chapman & Hall/CRC~~
	~~\| location = Boca Raton, FL~~
	~~\| title = The Structure of Complex Lie Groups~~
	~~\| url =~~ http://~~cs5517~~.~~userapi~~.com/~~u133638729/docs/55b6923279e2/c2611apb.pdf~~
	~~\| year = 2002}}~~
	*{{citation \| last=Serre \| first=Jean-Pierre \|title=Gèbres \|url=http://retro.seals.ch/digbib/view?~~rid=ensmat-001:1993:39::15 \|year~~=~~1993}}~~

	~~[[Category:Lie groups~~]]
	~~[[Category:Manifolds]]~~



	~~{{geometry~~-~~stub}}~~

en>Bgwhite: WP:CHECKWIKI error fix. Broken bracket problem. Do general fixes and cleanup if needed. - using AWB (9876)

2014-01-26T00:58:59Z

WP:CHECKWIKI error fix. Broken bracket problem. Do general fixes and cleanup if needed. - using AWB (9876)

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en>Ilmari Karonen: add short section anchors for easy linking

2012-06-18T10:40:48Z

add short section anchors for easy linking

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en>DavidCary: /* See also */ other related articles

en>NickPenguin: no consensus to merge

en>Bgwhite: WP:CHECKWIKI error fix. Broken bracket problem. Do general fixes and cleanup if needed. - using AWB (9876)

en>Ilmari Karonen: add short section anchors for easy linking