4 citations · 4 across the 4 of their papers we have counts for
5 papers
On connection between associators and 6j-symbols
Elena Lanina, Artem Novokhatnii, Alexey Sleptsov +1
We propose a new formula relating the rationalized Drinfeld associators obtained from the Knizhnik--Zamolodchikov equation to the quantum -symbols of the algebra $\mathcal{U}_q…
Algebraic structures of Vassiliev invariants for knot families
E. Lanina, A. Sleptsov
We explore algebraic relations on Vassiliev knot invariants related with correlators in the 3-dimensional Chern--Simons theory. Vassiliev invariants form infinite-dimensional algeb…
Can Yang-Baxter imply Lie algebra?
Dmitry Khudoteplov, Alexei Morozov, Alexey Sleptsov
Quantum knot invariants (like colored HOMFLY-PT or Kauffman polynomials) are a distinguished class of non-perturbative topological invariants. Any known way to construct them (via…
Construction of Lie algebra weight system kernel via Vogel algebra
Dmitry Khudoteplov, Elena Lanina, Alexey Sleptsov
We develop a method of constructing a kernel of Lie algebra weight system. A main tool we use in the analysis is Vogel's algebra and the surrounding framework. As an example of…
Closed 4-braids and the Jones unknot conjecture
Dmitriy Korzun, Elena Lanina, Alexey Sleptsov
The Jones problem is a question whether there is a non-trivial knot with the trivial Jones polynomial in one variable . The answer to this fundamental question is still unknown…