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Clifford algebra
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(Definition)
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Definition 0.1 Let us briefly define the notion of a Clifford algebra. Thus, let us consider first a pair  , where  denotes a real vector space and  is a quadratic form on  . Then, the Clifford algebra associated to  , is
denoted here as
 , is the algebra over
 generated by  , where for all
 , the relations:
 are satisfied; in particular,
 .
If  is an algebra and
 is a linear map satisfying
 then there exists a unique algebra homomorphism
 such that the diagram
commutes. (It is in this sense that
 is considered to be `universal').
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"Clifford algebra" is owned by bci1.
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(view preamble)
| Keywords: |
Clifford algebra |
Cross-references: commutes, diagram, homomorphism, relations, vector space
There are 2 references to this object.
This is version 5 of Clifford algebra, born on 2008-10-19, modified 2009-02-25.
Object id is 316, canonical name is CliffordAlgebra.
Accessed 303 times total.
Classification:
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Pending Errata and Addenda
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![$ \xymatrix{&&\hspace*{-1mm}{\rm Cl}(V)\ar[ddrr]^{\phi}&&\\ &&&&\\ \hspace{1mm} V \ar[uurr]^{{\rm Cl}} \ar[rrrr]_{c}&&&& W\hspace{1mm}}$](http://images.planetphysics.org/cache/objects/316/l2h/img16.png "$ \xymatrix{&&\hspace*{-1mm}{\rm Cl}(V)\ar[ddrr]^{\phi}&&\\ &&&&\\ \hspace{1mm} V \ar[uurr]^{{\rm Cl}} \ar[rrrr]_{c}&&&& W\hspace{1mm}}$")