3 papers
hep-th2025
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…
hep-th2025
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…
math.QA2025
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 o…