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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Real homogeneous algebras


Author: D. Ž. Djoković
Journal: Proc. Amer. Math. Soc. 41 (1973), 457-462
MSC: Primary 17A99
MathSciNet review: 0332902
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Abstract: Let $ (A,\mu )$ be a finite dimensional real algebra (not necessarily associative) with multiplication $ \mu \ne 0$. Assuming that $ \operatorname{Aut}(A)$ is transitive on one-dimensional subspaces we determine all such algebras. There are up to isomorphism only four such algebras, one in each of the dimensions 1, 3, 6, 7.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0332902-2
PII: S 0002-9939(1973)0332902-2
Keywords: Homogeneous algebra, Lie group, Lie algebra, linear representation, symmetric and skew-symmetric tensors, weights
Article copyright: © Copyright 1973 American Mathematical Society