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Infinite homogeneous algebras are anticommutative |
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| Authors: | Dragomir Z Dokovic Lowell G Sweet |
| Institution: | 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  . |
| Keywords: | Non-associative algebras automorphism group hypersurface |
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