Proceedings of the American Mathematical Society

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



On the triviality of homogeneous algebras over an algebraically closed field

Author: Lowell Sweet
Journal: Proc. Amer. Math. Soc. 48 (1975), 321-324
MSC: Primary 17E05
MathSciNet review: 0364382
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Abstract: Let $ A$ be a finite-dimensional algebra (not necessarily associative) over a field $ K$. Then $ A$ is said to be homogeneous if $ \operatorname{Aut} (A)$ acts transitively on the one-dimensional subspaces of $ A$. If $ A$ is homogeneous and $ K$ is algebraically closed, then it is shown that either $ {A^2} = 0$ or $ \dim A = 1$.

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Keywords: Homogeneous algebra, algebraically closed field, special nil algebra, Jordan normal form
Article copyright: © Copyright 1975 American Mathematical Society