Consensus (computer science) - Revision history

en>Gilo1969: fix citation(s) with wikilink(s) embedded in URL title

2014-12-08T10:36:36Z

fix citation(s) with wikilink(s) embedded in URL title

← Older revision		Revision as of 12:36, 8 December 2014
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	~~In mathematics, a~~ '~~''Chevalley basis''' for a [[Simple Lie group\|simple]] [[complex number\|complex]] [[Lie algebra]]~~ is		Oscar is how he's known as and he totally enjoys this name. He utilized to be unemployed but now he is a meter reader. One of the extremely very best things in the globe for me is to do aerobics and now I'm trying to earn money with it. Years ago we moved to Puerto Rico and my family enjoys it.<br><br>Take a look at my web site; at home std test ([http://vip.akwacity.com/oxwall/blogs/post/10278 click the next website page])
	a ~~[[Basis (linear algebra)\|basis]] constructed by [[Claude Chevalley]] with the property that all [[Algebra_over_a_field#Structure_coefficients\|structure constants]] are integers~~. ~~Chevalley used these bases to construct analogues~~ of ~~[[Lie group]]s over [[finite field]]s, called [[Chevalley group]]s.~~

	~~The generators of a Lie group are split into~~ the ~~generators ''H''~~ and '~~'E'' indexed by simple [[Root_system\|roots]]~~ and ~~their negatives <math>\pm\alpha_i</math>~~. ~~The relations among the generators are the following:~~

	:<~~math~~>~~[H_{\alpha_i},H_{\alpha_j}]=0~~<~~/math~~>
	~~:<math>[H_{\alpha_i},E_{\alpha_j}]=\alpha_j~~(~~H_{\alpha_i}) E_{\alpha_j}</math>~~
	~~:<math>~~[~~E_{-\alpha_i},E_{\alpha_i}] = H_{\alpha_i} </math>~~
	:~~<math>[E_{\beta},E_{\gamma}]=\pm(p+1)E_{\beta+\gamma}<~~/~~math>~~
	~~where the last relation is imposed only if <math>\beta + \gamma<~~/~~math> is a root and '''p''' is the greatest positive integer such that {{nowrap\|γ − ''p''β}} is a root~~. ~~The sign in~~ the ~~relation can be fixed arbitrarily.~~

	~~==References==~~
	*''Simple Groups of Lie Type'' by Roger W. Carter, ISBN 0-471-50683-4

	~~[[Category:Lie groups~~]]
	~~[[Category:Lie algebras]]~~


	~~{{algebra-stub}}~~

en>Monkbot: Fix CS1 deprecated date parameter errors

2014-02-04T06:01:18Z

Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 08:01, 4 February 2014
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	~~Royal Votaw~~ is ~~my title but I~~ by ~~no means really liked~~ that ~~title~~. ~~Delaware is the place I love most but I need~~ to ~~move for my family~~. ~~Bookkeeping is how he supports his family and his wage has been truly satisfying. One~~ of ~~my preferred hobbies is camping~~ and ~~now I~~'~~m attempting to earn cash with it~~.<br><br>~~Here is my webpage;~~ [~~http~~://~~User462~~.cp.~~isp169~~.~~com/?document_srl=148855 extended car warranty~~]		In mathematics, a '''Chevalley basis''' for a [[Simple Lie group\|simple]] [[complex number\|complex]] [[Lie algebra]] is
			a [[Basis (linear algebra)\|basis]] constructed by [[Claude Chevalley]] with the property that all [[Algebra_over_a_field#Structure_coefficients\|structure constants]] are integers. Chevalley used these bases to construct analogues of [[Lie group]]s over [[finite field]]s, called [[Chevalley group]]s.

			The generators of a Lie group are split into the generators ''H'' and ''E'' indexed by simple [[Root_system\|roots]] and their negatives <math>\pm\alpha_i</math>. The relations among the generators are the following:

			:<math>[H_{\alpha_i},H_{\alpha_j}]=0</math>
			:<math>[H_{\alpha_i},E_{\alpha_j}]=\alpha_j(H_{\alpha_i}) E_{\alpha_j}</math>
			:<math>[E_{-\alpha_i},E_{\alpha_i}] = H_{\alpha_i} </math>
			:<math>[E_{\beta},E_{\gamma}]=\pm(p+1)E_{\beta+\gamma}</math>
			where the last relation is imposed only if <math>\beta + \gamma</math> is a root and '''p''' is the greatest positive integer such that {{nowrap\|γ − ''p''β}} is a root. The sign in the relation can be fixed arbitrarily.

			==References==
			*''Simple Groups of Lie Type'' by Roger W. Carter, ISBN 0-471-50683-4

			[[Category:Lie groups]]
			[[Category:Lie algebras]]


			{{algebra-stub}}

129.132.210.31: /* Equivalency of agreement problems */

2012-07-10T11:18:05Z

Equivalency of agreement problems

New page

Royal Votaw is my title but I by no means really liked that title. Delaware is the place I love most but I need to move for my family. Bookkeeping is how he supports his family and his wage has been truly satisfying. One of my preferred hobbies is camping and now I'm attempting to earn cash with it.<br><br>Here is my webpage; [http://User462.cp.isp169.com/?document_srl=148855 extended car warranty]