Three dimensional homogeneous algebras

James A. MacDougall and Lowell G. Sweet

Vol. 74 (1978), No. 1, 153–162

DOI: 10.2140/pjm.1978.74.153

Abstract

An algebra A is homogeneous if its automorphism group acts transitively on the set of one dimensional subspaces of A. In this paper the structure of all three dimensional homogeneous algebra is determined. These fall into three classes: (1) truncated quaternion algebras over formally real Pythagorean fields; (2) an algebra over GF(2) in whlch x² = x for all x in A, and (3) two algebras over GF(2) which are generated by each of their nonzero elements. The automorphism group is determined in each case.

Mathematical Subject Classification 2000

Primary: 17A99

Milestones

Received: 1 February 1977

Revised: 21 July 1977

Published: 1 January 1978