A nonassociative algebra named after physicist Pascual Jordan which satisfies
 |
(1)
|
and
 |
(2)
|
The latter is equivalent to the so-called Jordan identity
 |
(3)
|
(Schafer 1996, p. 4). An associative algebra 
with associative product 
can be made into a Jordan algebra 
by the Jordan product
 |
(4)
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Division by 2 gives the nice identity 
, but it must be omitted in characteristic 
.
Unlike the case of a Lie algebra, not every Jordan algebra is isomorphic to a subalgebra of some 
. Jordan algebras which are isomorphic
to a subalgebra are called special Jordan algebras,
while those that are not are called exceptional
Jordan algebras.
