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Let be the Kac-Moody algebra associated to the affine Cartan matrix E is isomorphic to a quotient of the positive part of . We determine the isomorphism classes of nilpotent Lie algebras of type E

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This article deals with the evolution operator of evolution algebras. We give a theorem that allows to characterize these algebras when this operator is a homomorphism of algebras of rank n−2 and this result in turn allows us to extend the classification of this type of algebras, given in a previous result by ourselves in 2021, up to the case of dimension 4. For this purpose, we analyze and make use of an algorithm for the degenerate case. A computational study of the procedure is also made.