6 papers
Quantisation ideals, canonical parametrisations of the unipotent group and consistent integrable systems
M. A. Chirkov, A. V. Mikhailov, D. V. Talalaev
Using the methods of quantisation ideals, we construct a family of quantisations corresponding to Case alpha in Sergeev's classification of solutions to the tetrahedron equation. T…
On a family of Poisson brackets on gl(n) compatible with the Sklyanin bracket
Vladimir V. Sokolov, Dmitry V. Talalaev
In this paper, we study a family of compatible quadratic Poisson brackets on gl(n), generalizing the Sklyanin one. For any of the brackets in the family, the argument shift determi…
2-dimensional self-distributive non-counital bialgebras and knot invariants
Valeriy G. Bardakov, Tatiana A. Kozlovskaya, Alexander S. Panasenko +1
In the preprint of V. Bardakov, T. Kozlovskaya, D. Talalaev (Self-distributive bialgebras, arXiv:2501.19152) it was formulated a problem of classification of self-distributive bial…
Self-distributive algebras and bialgebras
Valeriy G. Bardakov, Tatiana A. Kozlovskaya, Dmitry V. Talalaev
This article is devoted to the study of self-distributive algebraic structures: algebras, bialgebras; additional structures on them, relations of these structures with Hopf algebra…
RE-algebras, quasi-determinants and the full Toda system
Dmitry V. Talalaev
In 1991, Gelfand and Retakh embodied the idea of a noncommutative Dieudonne determinant in the case of RTT algebra, namely, they found a representation of the quantum determinant o…
n-valued quandles and associated bialgebras
Valeriy G. Bardakov, Tatyana A. Kozlovskaya, Dmitry V. Talalaev
The principal aim of this article is to introduce and study n-valued quandles and n-corack bialgebras. We elaborate the basic methods of this theory, reproduce the coset constructi…