Infineta Systems - Revision history

en>Peaceray: Filling in 1 reference using Reflinks

2014-07-20T05:10:34Z

Filling in 1 reference using Reflinks

← Older revision		Revision as of 07:10, 20 July 2014
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	~~In mathematics~~, a '''braided''' vectorspace <math>\;V</math> is a [[vectorspace]] together with an additional structure map <math>\tau\;</math> symbolizing '''interchanging''' of two vector [[tensor product\|tensor copies]]:		I am Carlos from Altmunster studying Mathematics. I did my schooling, secured 83% and hope to find someone with same interests in Worldbuilding.<br><br>Feel free to visit my webpage :: basement renovation ideas ([http://www.homeimprovementdaily.com Learn Alot more Here])

	~~::<math>\tau:\; V\otimes V\longrightarrow V\otimes V \,</math>~~

	such that the [[Yang–Baxter equation]] is fulfilled. Hence drawing [[Penrose graphical notation\|tensor diagram]]s with <math>\tau\;</math> an '''overcorssing''' the corresponding composed morphism is unchanged when a [[Reidemeister move]] is applied to ~~the tensor diagram and thus they present a representation of the [[braid group]].~~

	~~As first example, every vector space is braided via the trivial braiding (simply flipping). A [[superspace]] has a braiding~~ with ~~negative sign~~ in ~~braiding two '''odd''' vectors~~. ~~More generally, a '''diagonal braiding''' means that for a~~ <~~math~~>~~\;V~~<~~/math~~>~~-base <math>x_i\;</math> we have~~

	::~~<math>\tau~~(~~x_i\otimes x_j)=q_{ij}(x_j\otimes x_i) \, </math>~~

	~~A good source for braided vector spaces entire~~ [[braided monoidal category\|braided monoidal categories]] with braidings between any objects <math>\tau_{V,W}\;</math>, most importantly the modules over [[quasitriangular Hopf algebra]]s and [[Yetter–Drinfeld category\|Yetter–Drinfeld modules]] over finite groups (such as <math>\mathbb{Z}_2</~~math> above)~~

	~~If <math>V\;<~~/~~math> additionally possesses an [[braided Hopf algebra\|algebra structure inside the braided category]] ("braided algebra") one has a '''braided commutator''' (e.g~~. ~~for a [[superspace]] the [[Commutator\|anticommutator]]):~~

	~~::<math>\;[x,y]_\tau:=\mu((x\otimes y)-\tau(x\otimes y))\qquad \mu(x\otimes y):=xy</math>~~

	~~Examples of such braided algebras (and even [[braided Hopf algebra\|Hopf algbebras]]) are the [[Nichols algebra]]s, that are by definition generated by a given braided vectorspace~~. ~~They appear as quantum Borel part of [[quantum group~~]~~]s and often (e.g. when finite or over an abelian group~~) possess an [[Root system\|arithmetic root system]], multiple [[Dynkin diagram]]s and a [[Poincare–Birkhoff–Witt theorem\|PBW-basis]] made up of braided commutators just like the ones in [[semisimple lie algebra]]s.

	~~<ref name=AS02>Andruskiewitsch, Schneider: ''Pointed Hopf algebras'', New directions in Hopf algebras, 1–68, Math. Sci. Res. Inst. Publ., 43, Cambridge Univ. Press, Cambridge, 2002.</ref>~~
	~~<references/>~~

	~~[[Category:Hopf algebras]]~~
	~~[[Category:Quantum groups]]~~


	~~{{algebra-stub}}~~

en>BattyBot: fixed CS1 errors: dates & General fixes using AWB (9816)

2013-12-25T01:17:00Z

fixed CS1 errors: dates & General fixes using AWB (9816)

← Older revision		Revision as of 03:17, 25 December 2013
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	~~Supplement your diet with vitamins that can fix the problem. Choose good fat~~, ~~especially those high in omega 3 fatty acids. Also, include chromium (~~a ~~natural anti-inflammatory source), selenium, Vitamin C and carotene. There are other even much more~~ [~~http://www.Encyclopedia.com/searchresults.aspx?q=potent+supplements potent supplements~~] ~~accessible that can help to target your joint pain and inflammation.~~<br><br>		In mathematics, a '''braided''' vectorspace <math>\;V</math> is a [[vectorspace]] together with an additional structure map <math>\tau\;</math> symbolizing '''interchanging''' of two vector [[tensor product\|tensor copies]]:

	~~[http~~:~~//relges.ch/Dpg relges.ch]~~<br><br>~~Consume at minimum twenty cherries daily, more if feasible. You can also drink cherry juice or consume dried cherries. Cherries have all-natural anti-inflammatory and antioxidant qualities~~.<br><br>~~Unfortunately, there are times~~ when it is ~~necessary~~ to ~~be treated Anti Inflammatory For Dogs with~~ a ~~lengthy-phraseroutine~~ of a ~~narcotic; maybeonethis kind of as Vicidin~~. ~~I have had to personally go viathis kind of an experience and it isn~~'~~t muchfun~~; ~~particularlywhile you are healing.~~<br><br>~~Pet pain is frequently remembered by the body in canines lengthy after the pain has finished. This means that things that~~ have ~~brought on discomfort in the past have the potential to cause even worse discomfort the next time the same factor happens. By attempting to reduce the quantities of pain that have been remembered~~, ~~pain killer~~ for ~~dogs can function much better and give~~ the ~~dog a much better general high quality of life~~ and ~~discomfort administration achievement.~~<br><br>~~And you know there~~'~~s a massive increase in cardiovascular disease, rheumatoid arthritis and Alzheimer~~'~~s in today~~'~~s world~~. ~~In fact, coronary heart illness is~~ the ~~#1 killer in The united states today.~~<br><br>~~Mats or knots should be untangled first utilizing your fingers before you comb them~~. ~~You spare your dog pain~~ as ~~nicely pain getting to wait for a lengthy time for you to finish brushing his coat~~. ~~Use a metal comb is much better in untangling the knots from the bottom~~. ~~Use~~ a ~~brush if~~ the ~~coat is mat and knot totally free~~.<br>~~<br>Have your dogs tooth skillfully cleaned~~. If, ~~for what at any time reason~~, ~~you dont want to or else you can't brush your canines tooth your self~~, get it into a veterinarian and also have the vet give the dogs tooth a expert cleaning. The vet will sedate your pup and do all the necessary scraping and cleaning of the teeth while the puppy is sleeping.<br><br>~~If you have virtually any inquiries about in which in addition to tips on how to utilize anti inflammatory pain medicine for dogs arthritis (~~[~~http~~:~~//tonisphere.com/sl/antiinflammatoryfordogs http~~:~~//tonisphere.com/~~]~~), you are able to e mail us at our internet site.~~		::<math>\tau:\; V\otimes V\longrightarrow V\otimes V \,</math>

			such that the [[Yang–Baxter equation]] is fulfilled. Hence drawing [[Penrose graphical notation\|tensor diagram]]s with <math>\tau\;</math> an '''overcorssing''' the corresponding composed morphism is unchanged when a [[Reidemeister move]] is applied to the tensor diagram and thus they present a representation of the [[braid group]].

			As first example, every vector space is braided via the trivial braiding (simply flipping). A [[superspace]] has a braiding with negative sign in braiding two '''odd''' vectors. More generally, a '''diagonal braiding''' means that for a <math>\;V</math>-base <math>x_i\;</math> we have

			::<math>\tau(x_i\otimes x_j)=q_{ij}(x_j\otimes x_i) \, </math>

			A good source for braided vector spaces entire [[braided monoidal category\|braided monoidal categories]] with braidings between any objects <math>\tau_{V,W}\;</math>, most importantly the modules over [[quasitriangular Hopf algebra]]s and [[Yetter–Drinfeld category\|Yetter–Drinfeld modules]] over finite groups (such as <math>\mathbb{Z}_2</math> above)

			If <math>V\;</math> additionally possesses an [[braided Hopf algebra\|algebra structure inside the braided category]] ("braided algebra") one has a '''braided commutator''' (e.g. for a [[superspace]] the [[Commutator\|anticommutator]]):

			::<math>\;[x,y]_\tau:=\mu((x\otimes y)-\tau(x\otimes y))\qquad \mu(x\otimes y):=xy</math>

			Examples of such braided algebras (and even [[braided Hopf algebra\|Hopf algbebras]]) are the [[Nichols algebra]]s, that are by definition generated by a given braided vectorspace. They appear as quantum Borel part of [[quantum group]]s and often (e.g. when finite or over an abelian group) possess an [[Root system\|arithmetic root system]], multiple [[Dynkin diagram]]s and a [[Poincare–Birkhoff–Witt theorem\|PBW-basis]] made up of braided commutators just like the ones in [[semisimple lie algebra]]s.

			<ref name=AS02>Andruskiewitsch, Schneider: ''Pointed Hopf algebras'', New directions in Hopf algebras, 1–68, Math. Sci. Res. Inst. Publ., 43, Cambridge Univ. Press, Cambridge, 2002.</ref>
			<references/>

			[[Category:Hopf algebras]]
			[[Category:Quantum groups]]


			{{algebra-stub}}

en>Ashwathk at 18:54, 30 August 2012

2012-08-30T18:54:12Z

New page

Supplement your diet with vitamins that can fix the problem. Choose good fat, especially those high in omega 3 fatty acids. Also, include chromium (a natural anti-inflammatory source), selenium, Vitamin C and carotene. There are other even much more [http://www.Encyclopedia.com/searchresults.aspx?q=potent+supplements potent supplements] accessible that can help to target your joint pain and inflammation. 

[http://relges.ch/Dpg relges.ch] Consume at minimum twenty cherries daily, more if feasible. You can also drink cherry juice or consume dried cherries. Cherries have all-natural anti-inflammatory and antioxidant qualities. Unfortunately, there are times when it is necessary to be treated Anti Inflammatory For Dogs with a lengthy-phraseroutine of a narcotic; maybeonethis kind of as Vicidin. I have had to personally go viathis kind of an experience and it isn't muchfun; particularlywhile you are healing. Pet pain is frequently remembered by the body in canines lengthy after the pain has finished. This means that things that have brought on discomfort in the past have the potential to cause even worse discomfort the next time the same factor happens. By attempting to reduce the quantities of pain that have been remembered, pain killer for dogs can function much better and give the dog a much better general high quality of life and discomfort administration achievement. And you know there's a massive increase in cardiovascular disease, rheumatoid arthritis and Alzheimer's in today's world. In fact, coronary heart illness is the #1 killer in The united states today. Mats or knots should be untangled first utilizing your fingers before you comb them. You spare your dog pain as nicely pain getting to wait for a lengthy time for you to finish brushing his coat. Use a metal comb is much better in untangling the knots from the bottom. Use a brush if the coat is mat and knot totally free. Have your dogs tooth skillfully cleaned. If, for what at any time reason, you dont want to or else you can't brush your canines tooth your self, get it into a veterinarian and also have the vet give the dogs tooth a expert cleaning. The vet will sedate your pup and do all the necessary scraping and cleaning of the teeth while the puppy is sleeping. If you have virtually any inquiries about in which in addition to tips on how to utilize anti inflammatory pain medicine for dogs arthritis ([http://tonisphere.com/sl/antiinflammatoryfordogs http://tonisphere.com/]), you are able to e mail us at our internet site.