Abstract
Two new necessary conditions for isomorphism between simple real Lie algebras are stated and proved, and are used, together with previously known necessary conditions and sufficient conditions, to investigate a new type of isomorphism between simple real Lie algebras. It is shown that three and only three examples of this type exist, of which one, the isomorphism between the Lie algebras of the groups SO(6,2) and ND 8, has not been noted previously. The existence of these examples is traced to certain exceptional properties of the groups of automorphisms of the corresponding simple complex Lie algebras A 1 and D 4.
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