Albert’s twisted field construction using division algebras with a multiplicative norm

This is the authors' abstract. We don't add key points for this paper.

We generalize Albert’s twisted field construction, applying it to unital division algebras with a multiplicative norm. We give conditions for the resulting algebras to be division algebras. Four- and eight-dimensional real unital and non-unital division algebras with large derivation algebras are constructed out of Hamilton’s quaternion and Cayley’s octonion algebra.