Equalization (audio): Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
No edit summary
m fix tags, replaced: <sup>2</sub> → <sup>2</sup> using AWB
Line 1: Line 1:
:''Standard resolution redirects here, for the television monitor size, see [[standard definition]]''
Yo bros  !!  Mijn naam is KEISHA KINGIk woon in   Vancouver  . Mijn leeftijd is  34. Naam van mijn school is   De Mimic Prep School<br><br>Also visit my weblog [http://www.rocktargatoitalia.com/divo/modules.php?name=Your_Account&op=userinfo&username=CUry inazuma eleven]
 
In mathematics, the '''standard complex''', also called '''standard resolution''', '''bar resolution''', '''bar complex''', '''bar construction''', is a way of constructing resolutions in [[homological algebra]]It was first introduced for the special case of algebras over a [[commutative ring]] by {{harvtxt|Eilenberg|Mac Lane|1953}} and {{harvtxt|Cartan|Eilenberg|1956|loc=IX.6}} and has since been generalized in many ways.
 
The name "bar complex" comes from the fact that {{harvtxt|Eilenberg|Mac Lane|1953}} used a vertical bar | as a shortened form of the tensor product ⊗ in their notation for the complex.
 
==Definition==
 
If ''A'' is an algebra over a field ''K'', the standard complex is
:<math>\cdots\rightarrow A\otimes A\otimes A\rightarrow A\otimes A\rightarrow A \rightarrow 0</math>
with the differential given by
:<math>d(a_0\otimes \cdots\otimes a_{n+1})=\sum_{i=0}^n (-1)^i a_0\otimes\cdots\otimes a_ia_{i+1}\otimes\cdots\otimes a_{n+1}</math>
 
==Normalized standard complex==
 
The normalized (or reduced) standard complex replaces ''A''⊗''A''⊗...⊗''A''⊗''A'' with
''A''⊗(''A''/''K'')⊗...⊗(''A''/''K'')⊗''A''.
 
==Monads==
{{Empty section|date=June 2011}}
 
==See also==
 
*[[Koszul complex]]
 
==References==
 
*{{Citation | last1=Cartan | first1=Henri | last2=Eilenberg | first2=Samuel | author2-link=Samuel Eilenberg | title=Homological algebra | url=http://books.google.com/books?id=0268b52ghcsC | publisher=[[Princeton University Press]] | series=Princeton Mathematical Series | isbn=978-0-691-04991-5  | mr=0077480 | year=1956 | volume=19}}
*{{Citation | last1=Eilenberg | first1=Samuel | author1-link=Samuel Eilenberg | last2=Mac Lane | first2=Saunders | author2-link=Saunders Mac Lane | title=On the groups of H(Π,n). I | jstor=1969820 | mr=0056295 | year=1953 | journal=[[Annals of Mathematics|Annals of Mathematics. Second Series]] | issn=0003-486X | volume=58 | pages=55–106}}
*{{cite arxiv | last1=Ginzburg | first1=Victor | title=Lectures on Noncommutative Geometry | eprint=math.AG/0506603 | year=2005}}
 
{{DEFAULTSORT:Standard Complex}}
[[Category:Homological algebra]]

Revision as of 00:18, 1 March 2014

Yo bros  !! Mijn naam is KEISHA KING. Ik woon in Vancouver . Mijn leeftijd is 34. Naam van mijn school is De Mimic Prep School

Also visit my weblog inazuma eleven