Abstract The notion of Rota-Baxter groups was recently introduced by Guo, Lang and Sheng
[19] in the geometric study of Rota-Baxter Lie algebras. They are closely related to skew …

The second cohomology group of a left skew brace with coefficients in a trivial left brace with
non-trivial actions is defined, its connection with extensions of a left skew brace by a trivial …

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 …

In this paper, we describe the split exact sequences of skew left braces. We define a free
action of the second cohomology group of a skew left brace H by Ann (I) on Ext α (H, I) and …

Relative Rota--Baxter groups, a generalization of Rota--Baxter groups, are closely
connected to skew left braces, which play a fundamental role in understanding non …

We generalise the construction of $ Q $-family of quandles and $ G $-family of quandles
which were introduced in the paper of A. Ishii, M. Iwakiri, Y. Jang, K. Oshiro, and find …

Quandles are self-distributive, right-invertible, idempotent algebras. A group with
conjugation for binary operation is an example of a quandle. Given a quandle $(Q,\ast) …

We present the following constructions: extension of a trivial quandle by a group with a
nontrivial abelian subgroup, a quandle over a noncommutative group by an arbitrary …

It is well-known that the cohomology of symmetric quandles generates robust cocycle
invariants for unoriented classical and surface links. Expanding on the recently introduced …

Considering the bijections of an arbitrary group onto itself which commute with all inner
automorphisms, we establish the general properties. In particular, the automorphisms …