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Jacobi identity |
This object's parent.
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Cross-references: Lie groups, composite, mappings, product, bilinear, vector space, ring of endomorphisms, polynomial rings, quaternions, ring, Cayley algebras, quotients, tensor algebras, Lie algebras, associative, unital, classes, algebras, composition, module, algebra, commutative ring
There are 7 references to this entry.
This is version 2 of algebra (module), born on 2002-12-31, modified 2005-04-14.
Object id is 3865, canonical name is AlgebraModule.
Accessed 5943 times total.
Classification:
| AMS MSC: | 16S99 (Associative rings and algebras :: Rings and algebras arising under various constructions :: Miscellaneous) | | | 20C99 (Group theory and generalizations :: Representation theory of groups :: Miscellaneous) | | | 13B99 (Commutative rings and algebras :: Ring extensions and related topics :: Miscellaneous) |
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Pending Errata and Addenda
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![[parent]](http://images.planetmath.org:8080/images/uparrow.png)
![$ [v,w]$](http://images.planetmath.org:8080/cache/objects/3865/l2h/img11.png "$ [v,w]$"){kind=small}
![$\displaystyle [v,v]=0\textrm{ for all }v\in M$](http://images.planetmath.org:8080/cache/objects/3865/l2h/img12.png "$\displaystyle [v,v]=0\textrm{ for all }v\in M$"){kind=small}
![$\displaystyle [v,[w,x]]+[w,[x,v]]+[x,[v,w]]=0\textrm{ for all }v,w,x\in M$](http://images.planetmath.org:8080/cache/objects/3865/l2h/img13.png "$\displaystyle [v,[w,x]]+[w,[x,v]]+[x,[v,w]]=0\textrm{ for all }v,w,x\in M$"){kind=small}
![$\displaystyle [v,w]+[w,v]=0\textrm{ for all }v,w\in M$](http://images.planetmath.org:8080/cache/objects/3865/l2h/img14.png "$\displaystyle [v,w]+[w,v]=0\textrm{ for all }v,w\in M$"){kind=small}