J. Austral. Math. Soc.  72 (2002), 47-56
A decomposition theorem for homogeneous algebras

 L. G. Sweet   Department of Mathematics   and Computer Science   University of Prince Edward Island   Charlottetown PEI C1A 4P3   Canada  sweet@upei.ca
and
 J. A. MacDougall   Department of Mathematics   University of Newcastle   Callaghan NSW 2308   Australia  mmjam@cc.newcastle.edu.au

Abstract
An algebra is homogeneous if the automorphism group of acts transitively on the one dimensional subspaces of . Suppose is a homogeneous algebra over an infinite field . Let denote left multiplication by any nonzero element . Several results are proved concerning the structure of in terms of . In particular, it is shown that decomposes as the direct sum . These results are then successfully applied to the problem of classifying the infinite homogeneous algebras of small dimension.