Witt's Theorem for Groups with Action and Free Leibniz Algebras

Abstract

Abstract A subcategory of the category of groups with action is determined and it is proved that the functor defined in [Datuashvili, Georgian Math. J. 9: 671–681, 2002] takes free objects from this category to free Leibniz algebras. This result gives a solution to a problem stated by J.-L. Loday [Enseign. Math. 39: 269–293, 1993], [K-Theory, 30: 105–127, 2003] and is an analogue of Witt's theorem for groups and Lie algebras [Witt, J. Reine Angew. Math. 1: 152–160, 1937].