Abstract In order to advance in the determination of all four-dimensional real division algebras , we introduce a new duplication process preserving the unit. This duplication process accompanied by an isotopy allow us to obtain all of these algebras in case Der( ) = {0} and partially in case Der( ) = {0}. In the last case, we provide an 8-parameter family of ugly ?-associative algebras and an 8-parameter family of ?-associative algebras whose group of automorphisms contains only the identity and some reflections. For non-ugly algebras ?f,f, the group Aut(?f,f) contains a reflection. Also algebras with Aut( ) = ?2 or ?2× ?2 are studied.
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