Idempotent Pre-Endomorphisms of Algebras
Rings and Algebras
2023-04-12 v1
Abstract
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 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.
Keywords
Cite
@article{arxiv.2304.05079,
title = {Idempotent Pre-Endomorphisms of Algebras},
author = {Fatma Azmy Ebrahim and Alberto Facchini},
journal= {arXiv preprint arXiv:2304.05079},
year = {2023}
}