How to Obtain Non-Flexible Quadratic Algebras as Mutation Algebras of Hurwitz Algebras

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 ∈ A \ F suitable. In particular, we thus obtain real eight-dimensional division algebras with large derivation algebras.