Given a general Hilbert space
, one can define an associated
-Clifford algebra,
, which admits a canonical representation
on
the bounded linear operators
on the Fock space
of
, (as in Plymen and Robinson, 1994), and hence one has a natural sequence of maps
The details and notation related to the definition of a
-Clifford algebra, are presented in the following
brief paragraph and diagram.
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').
Then, with the above notation, one has the precise definition of the
-Clifford algebra
as
when
where
Also note that the Clifford algebra is sometimes denoted as
.
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