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Rational Homogeneous Algebras
Published online by Cambridge University Press: 20 November 2018
Abstract
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 $\dim\,A\,>\,1$, then ${{A}^{2}}\,=\,0$.
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- Copyright © Canadian Mathematical Society 2012