Real homogeneous algebras

Djoković, D. Ž.

doi:10.1090/S0002-9939-1973-0332902-2

Real homogeneous algebras
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Proc. Amer. Math. Soc. 41 (1973), 457-462 Request permission

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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