8 problems

Let $C$ be a set, let $\boldsymbol{a}$ be a transitive $n\times n$ matrix with entries in $C$, and let $\mathbf r=\{r^{(c)}\}_{c\in C}\subset \mathfrak{g}\otimes\mathfrak{g}$ be a…

Necessity conjecture. All solutions of the classical Yang–Baxter equation are described by the preceding ansatz and differential-equation condition. The statement is presented as t…

Let $\mathfrak{g}$ be a Lie bialgebra with cobracket $\delta$, let $U(\mathfrak{g})$ denote its universal enveloping algebra, and let $A^{!}_{\mathcal{N}}$ be the $E_1$ Koszul dual…

Let $n$ be a positive integer, let ${\mathfrak g}$ be a Lie algebra, and let $r\in {\mathfrak g}\otimes {\mathfrak g}$ solve the classical Yang–Baxter equation (CYBE). Let…

Let $Q$ be a manifold and let $W$ be a Liouville domain. Write $\widehat{\mathbb{H}}_*^{S^1}\Lambda$ for Rabinowitz string homology, $S\mathbb{H}_*^{S^1}({\partial}W)$ for $S^1$-eq…

A Lie bialgebra is a vector space with a Lie bracket and a compatible Lie cobracket. Drinfeld's quantization conjecture. Any Lie bialgebra can be quantized. This conjecture asks wh…

Let $r_{BD}$ be an $r$-matrix from the list in Lemma, and let $\mathfrak{g}$ be the corresponding Lie algebra. Twisted Lie bialgebra structures on $\mathfrak{g}$ corresponding to…

Let $\mathfrak{g}$ be a simple Lie algebra, let $G=\operatorname{Ad}(\mathfrak{g})$ be its adjoint group, and let $r_{DJ}$ be the Drinfeld–Jimbo $r$-matrix. For a Belavin–Drinfeld…