Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Infinite homogeneous algebras
are anticommutative

Authors: Dragomir Z. Dokovic and Lowell G. Sweet
Journal: Proc. Amer. Math. Soc. 127 (1999), 3169-3174
MSC (1991): Primary 17D99; Secondary 17A36, 15A69
Published electronically: May 13, 1999
MathSciNet review: 1610948
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Abstract | References | Similar Articles | Additional Information

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 $x,y\in A$.

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Additional Information

Dragomir Z. Dokovic
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Lowell G. Sweet
Affiliation: Department of Mathematics, University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada C1A 4P3

Keywords: Non-associative algebras, automorphism group, hypersurface
Received by editor(s): January 7, 1998
Received by editor(s) in revised form: February 6, 1998
Published electronically: May 13, 1999
Additional Notes: This work was supported in part by the NSERC Grant A-5285.
Communicated by: Lance W. Small
Article copyright: © Copyright 1999 American Mathematical Society