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In [[mathematics]], a '''Poisson superalgebra''' is a '''Z'''<sub>2</sub>-[[graded algebra|graded]] generalization of a [[Poisson algebra]]. Specifically, a Poisson superalgebra is an (associative) [[superalgebra]] ''A'' with a [[Lie superbracket]]
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:<math>[\cdot,\cdot] : A\otimes A\to A</math>
such that (''A'', ,·]) is a [[Lie superalgebra]] and the operator
:<math>[x,\cdot] : A\to A</math>
is a [[superderivation]] of ''A'':
:<math>[x,yz] = [x,y]z + (-1)^{|x||y|}y[x,z].\,</math>
 
A supercommutative Poisson algebra is one for which the (associative) product is [[supercommutative algebra|supercommutative]].
 
This is one possible way of "super"izing the Poisson algebra. This gives the classical dynamics of fermion fields and classical spin-1/2 particles. The other is to define an [[antibracket algebra]] instead. This is used in the [[BRST quantization|BRST]] and [[Batalin-Vilkovisky]] formalism.
 
== Examples ==
 
* If ''A'' is any associative '''Z'''<sub>2</sub> graded algebra, then, defining a new product [.,.] (which is called the super-commutator) by [x,y]:=xy-(-1)<sup>|x||y|</sup>yx for any pure graded x, y turns ''A'' into a Poisson superalgebra.
 
==See also==
 
*[[Poisson supermanifold]]
 
==References==
*{{springer|id=p/p110170|title=Poisson algebra|author=Y. Kosmann-Schwarzbach}}
 
[[Category:Super linear algebra]]
[[Category:Symplectic geometry]]

Revision as of 17:04, 18 February 2014

Msvcr71.dll is an significant file that assists help Windows process different components of the system including important files. Specifically, the file is selected to help run corresponding files in the "Virtual C Runtime Library". These files are important in accessing any settings that support the different applications plus programs inside the system. The msvcr71.dll file fulfills countless significant functions; but it's not spared from getting damaged or corrupted. Once the file gets corrupted or damaged, the computer might have a difficult time processing and reading components of the system. However, consumers want not panic considering this problem might be solved by following several procedures. And I will show you certain tips about Msvcr71.dll.

Document files allow the consumer to input data, images, tables and other ingredients to enhance the presentation. The only problem with this structure compared to other file kinds such as .pdf for illustration is its ability to be easily editable. This means which anybody viewing the file will change it by accident. Additionally, this file structure is opened by alternative programs yet it does not guarantee that what you see inside the Microsoft Word application can nonetheless become the same whenever we see it using another program. However, it is still preferred by many computer consumers for its ease of utilize plus features.

The 'registry' is a central database which shops information, settings plus options for the computer. It's actually the many normal reason why XP runs slow and should you fix this issue, we can create the computer run a lot faster. The problem is that the 'registry' shops a lot of settings plus details about a PC... plus because Windows requires to use a lot of of these settings, any corrupted or damaged ones may straight affect the speed of the program.

Windows errors can be caused by any amount of reasons, however there's almost always one cause. There's a hidden part of your program that is responsible for creating 90% of all Windows mistakes, plus it's called the 'registry'. This is the central database for your program and is where your computer shops all its system files plus settings. It's a truly important part of Windows, which is needs to be able to function. However, it's furthermore among the largest causes of issues on a PC.

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It is critical which we remove obsolete registry entries from your program regularly, if you need a program to run faster, which is. If you don't keep your registry clean, a time usually come whenever the program can stop working completely. Then, the just way is to reformat the difficult drive plus start over!

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