Infinite homogeneous algebras are anticommutative
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- by Dragomir Ž. Đoković and Lowell G. Sweet PDF
- Proc. Amer. Math. Soc. 127 (1999), 3169-3174 Request permission
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 $x,y\in A$.References
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Additional Information
- Dragomir Ž. Đoković
- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
- Email: dragomir@herod.uwaterloo.ca
- Lowell G. Sweet
- Affiliation: Department of Mathematics, University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada C1A 4P3
- Email: sweet@upei.ca
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 3169-3174
- MSC (1991): Primary 17D99; Secondary 17A36, 15A69
- DOI: https://doi.org/10.1090/S0002-9939-99-04910-2
- MathSciNet review: 1610948