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In 2014, Wolfgang Rump showed that there exists a correspondence between leftnilpotent right R-braces and pre-Lie algebras. This correspondence, establishedusing a geometric approach related to flat affine manifolds and affine torsors,works locally. In this paper we explain Rump's correspondence using onlyalgebraic formulae. An algebraic interpretation of the correspondence works forfields of sufficiently large prime characteristic as well as for fields ofcharacteristic zero.

Algebraic approach to Rump's results on relations between braces and pre-Lie algebras