composition algebras over
There are infinitely many composition algebras over .
The other families of composition algebras also have an infinite number of non-isomorphic division algebras though the proofs are more involved. It suffices to show provide an infinite family of non-isometric quadratic forms of the form:
for rational numbers and . Such questions can involve complex number theory as for instance, if is a prime congruent to modulo then is isometric to and thus is isometric to for any other prime . But if then this cannot be said.
|Title||composition algebras over|
|Date of creation||2013-03-22 17:18:29|
|Last modified on||2013-03-22 17:18:29|
|Last modified by||Algeboy (12884)|