Infinite homogeneous algebras are anticommutative

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Title Infinite homogeneous algebras are anticommutative
Author(s) D. Z. Dokovic, Lowell G. Sweet
Journal Proceedings of the American Mathematical Society
Date 1999
Volume 127
Issue 11
Start page 3169
End page 3174
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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