3 papers
math.QA2026
Diagrammatic technique for Vogel's universality
D. Khudoteplov, A. Sleptsov
In his 1999 preprint "Universal Lie Algebra", P. Vogel put forward a hypothesis on the existence of a universal Lie algebra. Although this hypothesis remains open, it is known that…
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…