Biderivations of complete Leibniz algebras
Rings and Algebras
2025-10-21 v1 Differential Geometry
Abstract
If one wishes to define a complete Leibniz algebra in such a way as to extend the notion of a complete Lie algebra, two distinct definitions can be found in the current literature. Since biderivations on complete Lie algebras have already been studied, in order to extend those results and considering that Leibniz algebras are, among others, a natural generalisation of Lie algebras, we study here the biderivations of complete Leibniz algebras according to both definitions. In each case, we provide necessary and sufficient conditions for a bilinear map to be a biderivation of a Leibniz algebra. Finally, we analyse both symmetric and skew-symmetric biderivations, highlighting their structural properties.
Keywords
Cite
@article{arxiv.2510.16426,
title = {Biderivations of complete Leibniz algebras},
author = {Alfonso Di Bartolo and Francesco Paolo Di Fatta and Gianmarco La Rosa},
journal= {arXiv preprint arXiv:2510.16426},
year = {2025}
}