Geodesic
Rational Homogeneous Algebras
Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 351-354

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DOI

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 ${{A}^{2}}\,=\,0$ .
DOI : 10.4153/CMB-2011-087-5
Mots-clés : 17D99, 17A36, non-associative algebra, homogeneous, automorphism 
MacDougall, J. A.; Sweet, L. G. Rational Homogeneous Algebras. Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 351-354. doi: 10.4153/CMB-2011-087-5
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     title = {Rational {Homogeneous} {Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {351--354},
     year = {2012},
     volume = {55},
     number = {2},
     doi = {10.4153/CMB-2011-087-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-087-5/}
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