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 …

This book presents material in two parts. Part one provides an introduction to crossed
modules of groups, Lie algebras and associative algebras with fully written out proofs and is …

Loday's notoriously elusive “coquecigrues” are meant to relate to Leibniz algebras in the
same various ways that groups relate to Lie algebras. However, with the current approaches …

We investigate constructions of higher arity self-distributive operations, and give relations
between cohomology groups corresponding to operations of different arities. For this …

In this paper we focus on a certain self-distributive multiplication on coalgebras, which leads
to so-called rack bialgebra. We construct canonical rack bialgebras (some kind of …

We interpret augmented racks as a certain kind of multiplicative graphs and show that this
point of view is natural for defining rack homology. We also define the analogue of the group …

In this paper we focus on a certain self-distributive multiplication on coalgebras, which leads
to so-called rack bialgebra. Inspired by semi-group theory (adapting the Suschkewitsch …

The triad (groups, Lie algebras, associative bialgebras) plays a prominent role in
mathematics. The relations between Lie groups and Lie algebras, subsumed in Lie theory …

In this paper we focus on a certain self-distributive multiplication on coalgebras, which leads
to so-called rack bialgebra. Inspired by semi-group theory (adapting the Suschkewitsch …

Lie Algebroids in the Loday–Pirashvili Category⋆ Page 1 Symmetry, Integrability and
Geometry: Methods and Applications SIGMA 11 (2015), 079, 16 pages Lie Algebroids in the …