The Iterated Stieltjes Transform.

THEOREM 4. If Q is a Lie algebra of type All then n > 2 and $ SJ' where J is an i.a.a. of second kind in a simple algebra [. Thus a complete classification of Lie algebras of type A,, depends on the classification of simple associative algebras of second kind and of i.a.a.'s relative to cogredience in these algebras. It can be shown that the latter problem is essentially one of ordinary cogredience of hermitian matrices with coordinates in an involutorial division algebra of second kind. These questions are largely arithmetic in character and depend on the structure of 4'. A detailed account of this theory will appear in another journal.