Infinite homogeneous algebras are anticommutative
|Title||Infinite homogeneous algebras are anticommutative|
|Author(s)||D. Z. Dokovic, Lowell G. Sweet|
|Journal||Proceedings of the American Mathematical Society|
|Abstract||A (non-associative) algebra A, over a field k, is called homogeneous if its automorphism group permutes transitively the one dimensional subspaces of A. Suppose A is a nontrivial finite dimensional homogeneous algebra over an infinite field. Then we prove that x(2) = 0 for all x in A, and so xy = yx for all x; y is an element of A.|
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