Real division algebras with large automorphism group (Q1770523)

The possible types of Lie algebras of the automorphism group of a real division algebra have been determined by \textit{G. M. Benkart} and \textit{J. M. Osborn} [Am. J. Math. 103, 1135--1150 (1981; Zbl 0474.17002)]. The authors classify all 8-dimensional real division algebras whose automorphism group is either isomorphic to SO\((4)\) or contains a copy of SU\((2)\). They also construct a new 6 parameter family of 8-dimensional algebras whose automorphism group contains SO\((3)\) such that the algebra decomposes as the direct sum of a 3-dimensional and a 5-dimensional irreducible SO\((3)\)-submodule. The division algebras in this family form an open subset of the parameter space.