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1. CMB 2011 (vol 55 pp. 351)

MacDougall, J. A.; Sweet, L. G.
Rational Homogeneous Algebras
An algebra $A$ is homogeneous if the automorphism group of $A$ acts transitively on the one-dimensional subspaces of $A$. The existence of homogeneous algebras depends critically on the choice of the scalar field. We examine the case where the scalar field is the rationals. We prove that if $A$ is a rational homogeneous algebra with $\operatorname{dim} A>1$, then $A^{2}=0$.

Keywords:non-associative algebra, homogeneous, automorphism
Categories:17D99, 17A36

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