Clifford-Littlewood-Eckmann groups as orthogonal groups of forms of higher degree

Abstract

Forms of degree higher than 2 behave in a quite different way than quadratic forms. Jordan [J] proved finiteness of orthogonal groups of nonsingular forms of degree ^ 3, whereas it is known that quadratic forms, even if nonsingular, provide us mainly with infinite orthogonal groups. In this paper we describe the orthogonal groups of separable forms of degree at least 3 and for any Clifford-Littlewood-Eckmann group G we construct a form over the rational number field Q with the orthogonal group isomorphic to G.