2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225066Left-symmetric algebras have close relations with many important fields in mathematics and mathematical physics. Their classification is very complicated due to the nonassociativity. In this paper, we re-study the correspondence between left-symmetric algebras and the bijective 1-cocycles. Then a procedure is provided to classify left-symmetric algebras in terms of classification of equivalent classes of bijective 1-cocycles. As an example, the 3-dimensional complex left-symmetric algebras are classified.35 pagesQuantum AlgebraRings and Algebras17B, 81Rtext