Abstract
We present an elementary way to obtain new families of division algebras of degree n out of division algebras with a multiplicative norm. Families of four- and eight-dimensional non-flexible quadratic division algebras over a field F of characteristic not 2 are easily constructed as a-mutation algebras of Hurwitz division algebras A over F, choosing \({a \in A \setminus F}\) suitable. In particular, we thus obtain real eight-dimensional division algebras with large derivation algebras.
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