Vol. 59, No. 2, 1975

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On doubly homogeneous algebras

Lowell G. Sweet

Vol. 59 (1975), No. 2, 595–597

The algebras to be discussed are assumed to be finite dimensional and not necessarily associative. If A is an algebra over a field K let Aut (A) denote the group of algebra automorphisms of A. We define A to be doubly homogeneous if Aut (A) is doubly transitive on the one-dimensional subspaces of A. Also a doubly homogeneous algebra A is said to be nontrivial if A20 and dimension A > 1. It is shown that the only nontrivial doubly homogeneous algebra is unique up to isomorphism.

Mathematical Subject Classification 2000
Primary: 17A99
Received: 13 September 1974
Revised: 21 November 1974
Published: 1 August 1975
Lowell G. Sweet