Rational homogeneous algebras (Q2888789)

A finite dimensional algebra \(A\) over a field is called homogeneous if the automorphism group of \(A\) acts transitively on the one-dimensional subspaces of \(A\). All finite homogeneous algebras and all homogeneous algebras over the field of real numbers are known. The authors show that every at least two-dimensional homogeneous algebra over the field of rational numbers is trivial, i.e. there holds \(x y = 0\) for all \(x,y \in A\).