Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 ; Department of Mathematics, University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada C1A 4P3
Abstract:
A (non-associative) algebra , over a field , is called homogeneous if its automorphism group permutes transitively the one dimensional subspaces of . Suppose is a nontrivial finite dimensional homogeneous algebra over an infinite field. Then we prove that for all in , and so for all .