6 papers · 1 filter
Algebra, group, and Hopf Rota-Baxter operators
Valeriy G. Bardakov, Igor M. Nikonov, Viktor N. Zhelaybin
We know definition of Rota--Baxter operators on different algebraic systems. For examples, on groups, on algebras, on Hopf algebras. On some algebraic systems it is possible to def…
Orders of products of horizontal class transpositions
V. G. Bardakov, A. L. Iskra
The class transposition group was introduced by S. Kohl in 2010. It is a countable subgroup of the permutation group of the set of integers $\mat…
Lie Rota--Baxter operators on the Sweedler algebra
Valeriy G. Bardakov, Igor M. Nikonov, Viktor N. Zhelaybin
If is an associative algebra, then we can define the adjoint Lie algebra and Jordan algebra . It is easy to see that any associative Rota--Baxter operator on…
Some properties of relative Rota--Baxter operators on groups
V. G. Bardakov, T. A. Kozlovskaya, P. P. Sokolov +2
We find connection between relative Rota--Baxter operators and usual Rota--Baxter operators. We prove that any relative Rota--Baxter operator on a group with respect to $(G, Ψ…
Extensions of braid group representations to the monoid of singular braids
Valeriy G. Bardakov, Nafaa Chbili, Tatyana A. Kozlovskaya
Given a representation of the braid group , into a group , we are considering the problem of whether it is possible to extend this repre…
Rota--Baxter and averaging operators on racks and rack algebras
V. G. Bardakov, V. A. Bovdi
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 averag…