Traced monoidal category - Revision history

en>Wikidsp: either the picture or the text had to change, and I can't change the picture.

2014-03-17T11:44:05Z

either the picture or the text had to change, and I can't change the picture.

← Older revision		Revision as of 13:44, 17 March 2014
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	~~In [[abstract algebra]], a '''Koszul algebra''' <math>R</math>~~ is ~~a [[graded algebra\|graded]] <math>k</math>-[[algebra over a field\|algebra]] over which the [[ground field]] <math>k</math> has a linear minimal graded free resolution, ''i~~.~~e.'', there exists an [[exact sequence]]:~~		Greetings! I am Myrtle Shroyer. South Dakota is her beginning location but she requirements to move because of her family. Body developing is what my family members and I appreciate. He utilized to be unemployed but now he is a meter reader.<br><br>my web site: std home test ([http://dateplate.com/dayzfe click through the following web page])

	~~:<math>\cdots \rightarrow R(-i)^{b_i} \rightarrow \cdots \rightarrow R(-2)^{b_2} \rightarrow R(-1)^{b_1} \rightarrow R \rightarrow k \rightarrow 0.</math>~~
	It is ~~named after the French mathematician [[Jean-Louis Koszul]]~~.

	~~We can choose bases for the free modules in the resolution; then the maps can~~ be ~~written as matrices. For a Koszul algebra, the entries in the matrices are zero or linear forms.~~

	~~An example of a Koszul algebra~~ is a ~~[[polynomial ring]] over a field, for which the [[Koszul complex]] is the minimal graded free resolution of the ground field~~. ~~There are Koszul algebras whose ground fields have infinite minimal graded free resolutions, ''e.g'',~~ <~~math~~>~~R = k[x,y]/(xy)~~ <~~/math~~>

	~~== References ==~~
	* R. Froberg, ''[http://altenua.udea.edu.co/heragis/koszulalgfroberg.pdf Koszul Algebras]'', In: Advances in Commutative Ring Theory. Proceedings of the 3rd International Conference, Fez, Lect. Notes Pure Appl. Math. '''205''', Marcel Dekker, New York, 1999, pp. 337–350.
	* J.-L. Loday, B. Vallette ''[http://math.unice.fr/~brunov/Operads.pdf Algebraic Operads]'', Springer, 2012.
	* A. Beilinson, V. Ginzburg, W. Soergel, "[http:~~//www.ams.org/journals/jams/1996-9-02/S0894-0347-96-00192-0/S0894-0347-96-00192-0.pdf Koszul duality patterns in representation theory]", ''J. Amer. Math. Soc.'' '''9'''~~ (~~1996) 473–527.~~
	* V. Mazorchuk, S. Ovsienko, C. Stroppel, "[http://~~www~~.~~ams.org~~/~~journals/tran/2009-361-03/S0002-9947-08-04539-X/ Quadratic duals, Koszul dual functors, and applications~~]~~", ''Trans. of the AMS'' '''361''' (2009~~) ~~1129-1172.~~

	~~[[Category:Algebras]]~~


	~~{{algebra-stub}}~~

en>ChrisGualtieri: General Fixes using AWB

2013-10-20T03:30:54Z

General Fixes using AWB

← Older revision		Revision as of 05:30, 20 October 2013
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	Hi there. ~~My name~~ is ~~Sophia Meagher even though it~~ is ~~not~~ the ~~live psychic reading~~ ([http://~~netwk~~.~~hannam~~.ac.kr/xe/~~data_2/85669 netwk~~.~~hannam~~.ac.~~kr]) title on my beginning certification~~. ~~Office supervising is exactly where her main income arrives from but she~~'~~s already utilized for an additional 1~~. ~~My spouse and I live in Mississippi and I adore each working day living right here~~. It'~~s not a common factor but what she likes performing is to perform domino but she doesn~~'~~t have the time recently.<br><br>Here is my blog post: psychic love readings (~~[http://~~brazil~~.~~amor-amore~~.~~com~~/~~irboothe Click On this website~~]~~) psychic readings online (~~[http://~~afeen~~.~~fbho~~.~~net~~/v2/~~index.php?do=~~/~~profile~~-~~210~~/~~info~~/ http://~~afeen~~.~~fbho~~.~~net~~])		In [[abstract algebra]], a '''Koszul algebra''' <math>R</math> is a [[graded algebra\|graded]] <math>k</math>-[[algebra over a field\|algebra]] over which the [[ground field]] <math>k</math> has a linear minimal graded free resolution, ''i.e.'', there exists an [[exact sequence]]:

			:<math>\cdots \rightarrow R(-i)^{b_i} \rightarrow \cdots \rightarrow R(-2)^{b_2} \rightarrow R(-1)^{b_1} \rightarrow R \rightarrow k \rightarrow 0.</math>
			It is named after the French mathematician [[Jean-Louis Koszul]].

			We can choose bases for the free modules in the resolution; then the maps can be written as matrices. For a Koszul algebra, the entries in the matrices are zero or linear forms.

			An example of a Koszul algebra is a [[polynomial ring]] over a field, for which the [[Koszul complex]] is the minimal graded free resolution of the ground field. There are Koszul algebras whose ground fields have infinite minimal graded free resolutions, ''e.g'', <math>R = k[x,y]/(xy) </math>

			== References ==
			* R. Froberg, ''[http://altenua.udea.edu.co/heragis/koszulalgfroberg.pdf Koszul Algebras]'', In: Advances in Commutative Ring Theory. Proceedings of the 3rd International Conference, Fez, Lect. Notes Pure Appl. Math. '''205''', Marcel Dekker, New York, 1999, pp. 337–350.
			* J.-L. Loday, B. Vallette ''[http://math.unice.fr/~brunov/Operads.pdf Algebraic Operads]'', Springer, 2012.
			* A. Beilinson, V. Ginzburg, W. Soergel, "[http://www.ams.org/journals/jams/1996-9-02/S0894-0347-96-00192-0/S0894-0347-96-00192-0.pdf Koszul duality patterns in representation theory]", ''J. Amer. Math. Soc.'' '''9''' (1996) 473–527.
			* V. Mazorchuk, S. Ovsienko, C. Stroppel, "[http://www.ams.org/journals/tran/2009-361-03/S0002-9947-08-04539-X/ Quadratic duals, Koszul dual functors, and applications]", ''Trans. of the AMS'' '''361''' (2009) 1129-1172.

			[[Category:Algebras]]


			{{algebra-stub}}

en>Rjwilmsi: /* References */ 10.1017/S0305004100074338

2011-07-16T18:41:32Z

References: 10.1017/S0305004100074338

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Hi there. My name is Sophia Meagher even though it is not the live psychic reading ([http://netwk.hannam.ac.kr/xe/data_2/85669 netwk.hannam.ac.kr]) title on my beginning certification. Office supervising is exactly where her main income arrives from but she's already utilized for an additional 1. My spouse and I live in Mississippi and I adore each working day living right here. It's not a common factor but what she likes performing is to perform domino but she doesn't have the time recently.<br><br>Here is my blog post: psychic love readings ([http://brazil.amor-amore.com/irboothe Click On this website]) psychic readings online ([http://afeen.fbho.net/v2/index.php?do=/profile-210/info/ http://afeen.fbho.net])