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Ebrahim, Fatma Azmy; Facchini, Alberto
Communications in algebra, 02/2024, Volume: 52, Issue: 2Journal Article
In the study of pre-Lie algebras, the concept of pre-morphism arises naturally as a generalization of the standard notion of morphism. Pre-morphisms can be defined for arbitrary (not-necessarily associative) algebras over any commutative ring k with identity, and can be dualized in various ways to generalized morphisms (related to pre-Jordan algebras) and anti-pre-morphisms (related to anti-pre-Lie algebras). We consider idempotent pre-endomorphisms (generalized endomorphisms, anti-pre-endomorphisms). Idempotent pre-endomorphisms are related to semidirect-product decompositions of the sub-adjacent anticommutative algebra.
