Vol. 59, No. 2, 1975

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ISSN: 0030-8730
On doubly homogeneous algebras

Lowell G. Sweet

Vol. 59 (1975), No. 2, 595–597
Abstract

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
Milestones
Received: 13 September 1974
Revised: 21 November 1974
Published: 1 August 1975
Authors
Lowell G. Sweet