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) |
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.
