T. Datuashvili

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

Abstract:
A subcategory of the category of groups with action is determined and it is proved that the functor defined by the author earlier (2002) takes free objects from this category to free Leibniz algebras. This result gives a solution to a problem stated by J.-L. Loday (1993, 2003) and is an analogue of Witt's theorem for groups and Lie algebras (1937).

Keywords:
Central series, groups, groups with action on itself, Lie algebras, Leibniz algebras, Lie-Leibniz algebras.

MSC 2000: 17B60