Abstract
Natural generalizations of the quaternion algebra called quaternionlike algebras (ql algebras) are considered. The notion of a Lie algebra induced by a ql algebra is introduced and a classification of such Lie algebras is presented. It is shown that local Lie groups defined by Lie algebras induced by ql algebras exhaust, with accuracy to local isomorphisms, all local Lie groups endowed with some simple composition laws of their local parameters.
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