This paper reviews the properties and applications of certain n-ary generalizations of Lie
algebras in a self-contained and unified way. These generalizations are algebraic structures …

Cet article apporte une solution locale au problème des coquecigrues pour les algèbres de
Leibniz. Ce problème consiste à trouver une généralisation de la structure de groupe (de …

Loday introduced the notion of a dimonoid and constructed the free dimonoid. The paper
concerns the variety theory of dimonoids. We recall and summarize the results obtained by …

We associate to every quandle X and an associative ring with unity k, a nonassociative ring
k [X] following [3]. The basic properties of such rings are investigated. In particular, under the …

A bstract We extend the notion of Lie bialgebroids for more general bracket structures used
in string and M theories. We formalize the notions of calculus and dual calculi on algebroids …

In this paper, we use the local integration of a Leibniz algebra h using a Baker–Campbell–
Hausdorff type formula in order to deformation quantize its linear dual h⁎. More precisely …

The integration problem of a C-bracket and a Vaisman (metric, pre-DFT) algebroid that are
geometric structures of double field theory (DFT) is analyzed. We introduce a notion of a pre …

In the present article we define and investigate relative Rota--Baxter operators and relative
averaging operators on racks and rack algebras. Also, if B is a Rota--Baxter or averaging …

Global integration of Leibniz algebras Page 1 HAL Id: hal-01392779 https://hal.science/hal-01392779
Submitted on 9 Nov 2016 HAL is a multi-disciplinary open access archive for the deposit and …

We interpret the complexes defining rack cohomology in terms of a certain dg bialgebra.
This yields elementary algebraic proofs of old and new structural results for this cohomology …