Two-groups and Jordan algebras

James Edward Ward

Vol. 32 (1970), No. 3, 821–829

DOI: 10.2140/pjm.1970.32.821

Abstract

Stroud and Paige have introduced an important class of central simple Jordan algebras B(2ⁿ) of characteristic two. This paper determines the automorphism groups of the algebras B(2ⁿ) and, in so doing, produces an infinite family of finite 2-groups. This is accomplished by characterizing the automorphisms of B(2ⁿ) as matrices operating on the natural basis for the underlying vector space of B(2ⁿ) and then using this characterization to obtain generators and commuting relations for the automorphism groups.

Mathematical Subject Classification

Primary: 17.40

Milestones

Received: 21 May 1969

Published: 1 March 1970