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math.RA2024
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…
math.RA2021
On the solvability of graded Novikov algebras
Ualbai Umirbaev, Viktor Zhelyabin
We show that the right ideal of a Novikov algebra generated by the square of a right nilpotent subalgebra is nilpotent. We also prove that a -graded Novikov algebra over a f…