New Simple Lie Algebras of Type Z>4 by H. P. Allen and J. C. Ferrar

This brief note is to demonstrate the existence of a new class of (exceptional) Lie algebras of type D^ The construction stems from a cyclic sixth degree extension P /$ , together with an element y of norm 1 in the unique cubic subfield F/$ of P /$ , where y(£NPf!?(P*). Each such y will determine a non-Jordan (see [l] for definition) Lie algebra 8(7), of type D4111. Two algebras of this form, 8(7) and 8(p), will be isomorphic if and only if 7 differs from a conjugate of p by a norm in NP/F(P*). The possibility of obtaining new £Vs from such a construction was first conjectured in [2]. We shall make free use of the well-known theory of finite Galois descent for nonassociative algebras and all the results which we use may be found in ([5, Chapter 10]).