On doubly homogeneous algebras

Lowell G. Sweet

Vol. 59 (1975), No. 2, 595–597

DOI: 10.2140/pjm.1975.59.595

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 A²≠0 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