16 problems

Let $\mathfrak g(\infty)$ be a locally simple Lie algebra, and let $\operatorname{U}(\mathfrak g(\infty))$ be its universal enveloping algebra. An augmentation ideal is an ideal ar…

Let $\fg$ be a simple $\mathbb{Z}$-graded Lie algebra of polynomial growth (GLAPG type). Let $\fvect(1):=\fder\,\Cee[x]$ and $\fwitt$, equivalently…

Let $\mathfrak g$ be one of $V\!ir$, $W$, or $W_{\geq -1}$. For a local function $\chi\in\mathfrak g^*$, choose a polarization and form the annihilator of the induced module; write…

Dicksonianity conjecture. Then $\mathfrak g$ is Dicksonian.

Positive Witt algebra ideal ACC conjecture. The system of two-sided ideals of $U(W_+)$ satisfies the ascending chain condition.

Let $U(\mathfrak{o}(\infty))$ and $U(\mathfrak{sp}(\infty))$ be the universal enveloping algebras of the infinite-dimensional orthogonal and symplectic Lie algebras. Let … be the i…

Let $U(\mathfrak{o}(\infty))$ be the universal enveloping algebra of the infinite-dimensional orthogonal Lie algebra, and call a primitive ideal integrable when it arises from an i…

Let $\frak{g}=\frak{o}(\infty)$ or $\frak{sp}(\infty)$, and let $M$ be a finitely generated object of the large annihilator category $\cal{OLA}$. Annihilator conjecture. The annihi…

Let $\Phi[\sigma;1;f]$ be the limiting object considered in the paper, and let $(\mathfrak l_{k_h})_h$ be the system of dynamical symmetry Lie algebras associated with the embeddin…

Let $\mathfrak g(\infty)$ be one of the locally simple Lie algebras $\mathfrak{sl}(\infty)$, $\mathfrak o(\infty)$, or $\mathfrak{sp}(\infty)$. Consider its universal enveloping al…

Equivalence conjecture. The functor

Let $V$ be a countable-dimensional vector space, let $\mathfrak{g}=\mathfrak{sl}(V,V_*)$, $\mathfrak{o}(V)$, or $\mathfrak{sp}(V)$, and let $\mathfrak{g}^M$ be the corresponding Ma…

Assume that $\mathfrak{g}$ is a non-diagonal Lie algebra and that $\mathfrak{h}$ is the relevant local Cartan subalgebra. Triviality conjecture. The category…

Let $\widetilde{{\frak{gl}}}_{\infty}^{e}$ be the extended affine Lie algebra considered in the construction, let $\ell\in\mathbb C$ be a level, and let…

Let $\mathcal{L}=\bigoplus_{n\in\mathbb{Z}}\mathcal{L}_n$ be a simple graded Lie algebra such that $\operatorname{dim}\mathcal{L}_n=1$ for every $n\in\mathbb{Z}$. Kac's classificat…

Let $M_0$ be the model infinite filiform Lie algebra with basis $a,e_1,e_2,\ldots$, and let a deformation be specified by coefficients $\lambda_{js}$ in … for all $j\geq 1$, where…