7 problems

Vogel's conjecture. The multiplication on $\Lambda$ is abelian, and $\Lambda$ is isomorphic to the polynomial algebra $R_0$. The $\Lambda$-algebra and its action on spaces of diagr…

A Jacobi diagram is a uni-trivalent graph equipped with the additional structure used in the theory of Vassiliev invariants. Its legs are its univalent vertices. Odd-leg vanishing…

Let $\Bbbk\mathbf{gr}^{\operatorname{op}}$ be the opposite-category module category associated with the handlebody Jacobi-diagram category, and let $A^{L}_d Q$ denote the submodule…

Lando–Yang conjecture. The projection $u(D)$ is a linear combination of connected Jacobi diagrams with at most $tau(D)$ legs. In particular, for any Lie algebra $bfg$ and its asso…

Let $\Lambda$ be Vogel's algebra of three-legged Jacobi diagrams that are antisymmetric under permutations of their legs, with product defined by insertion at a vertex. Generation…

Let $\mathcal{X}^3$ be the space of fixed Jacobi diagrams with three legs, and let $\Lambda\subseteq\mathcal{X}^3$ be the subspace of elements antisymmetric under permutations of t…

Let $\mathcal{B}$ be the vector space of open Jacobi diagrams modulo the antisymmetry and IHX relations, with univalent vertices called legs. Odd-leg conjecture. Any diagram with a…