Four-dimensional homogeneous algebras

Lowell G. Sweet and James A. MacDougall

Vol. 129 (1987), No. 2, 375–383

DOI: 10.2140/pjm.1987.129.375

Abstract

An algebra is homogeneous if the automorphism group acts transitively on the one dimensional subspaces of the algebra. The purpose of this paper is to determine all homogeneous algebras of dimension 4. It continues previous work of the authors in which all homogeneous algebras of dimensions 2 and 3 were described. Our main result is the proof that the field must be GF(2) and the algebras are of a type previously described by Kostrikin. There are 5 non-isomorphic algebras of dimension 4; a description of each is given and the automorphism group is calculated in each case.

Mathematical Subject Classification 2000

Primary: 17A01

Secondary: 17A35

Milestones

Received: 11 January 1985

Published: 1 October 1987