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Composition algebra
In
mathematics
, a
composition algebra
over a
field
is a
not necessarily associative
algebra
over together with a
nondegenerate
quadratic form
which satisfies
for all and in .
Unital
composition algebras are called
Hurwitz algebras
. If the ground field is the field of
real numbers
and is
positive-definite
, then is called an
Euclidean Hurwitz algebra
.
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