Abstract
In order to advance in the determination of all four-dimensional real division algebras 𝒜, 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(𝒜) = {0} and partially in case Der(𝒜) = {0}. In the last case, we provide an 8-parameter family of ugly ℂ-associative algebras and an 8-parameter family of ℂ-associative algebras whose group of automorphisms contains only the identity and some reflections. For non-ugly algebras ℍf,f, the group Aut(ℍf,f) contains a reflection. Also algebras 𝒜 with Aut(𝒜) = ℤ2 or ℤ2 × ℤ2 are studied.
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