15 problems

Let $\widehat{\mathfrak{krv}}_2$ be the Kashiwara–Vergne Lie algebra, let $\mathfrak{grt}_1$ be the Grothendieck–Teichmüller Lie algebra, and let $\mathfrak{t}_2$ be the two-strand…

Let $\mathfrak g$ be a finite-dimensional Lie algebra, let $n$ be a positive integer, and let $x_1,\ldots,x_n\in\mathfrak g$. Define … For each $i$, let $\partial_{x_i}F_i$ be the…

Let $k$ be the coefficient field, let $mathfrak{fr}k(x0,x1)$ be the completed free Lie algebra on $x0,x1$, and let $psi{451}$, $psi{123}$, and $l^{y,x}{(a1,dots,am),(b1,dots,bn)}$…

Let $\widehat{\mathfrak{lkv}}_2$ be the linearized Kashiwara–Vergne Lie algebra, bigraded by weight and depth. Let $\mathrm{BK}_{W,D}$ be the coefficients defined by … with $s,t$ f…

Let the four Lie algebras in the inclusions referred to in the source be graded by weight, and let the associated graded Lie algebras for the depth filtration be included as in the…

Motivic Grothendieck–Teichmüller criterion. The inclusion

Hodge-theoretic realization conjecture. The inclusion

Let $ARI_{al+push/circneut}$ denote the space of moulds satisfying alternality, push-invariance, and circ-neutrality, and let $swap$ be the swap operation. For…

Let $ARI_{al+push/circneut}$ be the space of moulds satisfying alternality, push-invariance, and circ-neutrality, and let $swap$ denote the swap operation. Theorem … is an isomorph…

Let $\mathfrak{krv}$, $\mathfrak{ds}$, $\mathfrak{lkv}$, and $\mathfrak{ls}$ denote the Kashiwara–Vergne, double-shuffle, linearized Kashiwara–Vergne, and linearized double-shuffle…

For each integer $k\geq 1$, let $\widehat{\mathfrak{krv}}^{(k)}_2$ and $\widehat{\mathfrak{krv}}^{(k+1)}_2$ denote the successive filtered Kashiwara–Vergne Lie algebras. Stabilizat…

Injection conjecture. The Lie algebra $\mathfrak{grt}_{\rm ell}$ injects into $\mathfrak{krv}^{(1,1)}$. This conjecture is motivated by the preceding proposition, which gives an in…

Generalized Kashiwara–Vergne conjecture. There exists a group automorphism $P:\exp\mathfrak F_2\to\exp\mathfrak F_2$ such that $P\in T\operatorname{Aut}\exp\mathfrak F_2$,

Let $p>2$ be a prime and let $\mathbb{K}$ be a field of characteristic $p$. Let $A(x,y)$ and $B(x,y)$ be solutions of the partial Kashiwara–Vergne equations, chosen symmetrically s…

Let $\widehat{\operatorname{\mathfrak{kv}}}_2$ be the completed Kashiwara–Vergne Lie algebra, let $\operatorname{\mathfrak{grt}}$ be the Grothendieck–Teichmüller Lie algebra, and l…