14 problems

Let $G$ be a finite simple group, and let $\widetilde G$ denote its universal central extension. Wilson's conjecture. The group $\widetilde G$ has a presentation with $2$ generator…

Central-extension bounded-locality conjecture. The locality function $S_{\widehat{\goth L},\,\cal G\cup\cal M}$ is also uniformly bounded.

Feigin–Novikov conjecture. Every cocycle of the vector field algebra is cohomologous to a linear combination of geometric cocycles obtained by integration along the basis cycles in…

Let $A=\mathbb{C}[x^{\pm1},u\mid u^2=P(x)]$, where $P(x)\in\mathbb{C}[x]$ is palindromic of even degree $2r$ with simple roots. Let $A/\partial A$ denote the quotient by exact deri…

Let $\mathcal{M}$ be a bulk internal manifold, let $\mathfrak{g}(\mathcal{M})$ be its generalized Kac–Moody current algebra, and let its cohomological 2-cocycles be computed from b…

Let $\mathcal{M}$ be a compact manifold, let $\mathfrak{g}$ be the relevant finite-dimensional algebra, for example $E_{d(d)}$, and let $L^{2}(\mathcal{M})$ provide a basis. Let…

Let $\mathcal{M}$ be an internal manifold with isometries, and let $\mathfrak{g}(\mathcal{M})$ be its generalized Kac–Moody current algebra. Let fluxes be pulled back to…

Let $\mathcal{M}$ be an internal manifold with isometries, let $\mathfrak{g}(\mathcal{M})$ be its generalized Kac–Moody current algebra, and let flux backgrounds define the reduced…

Let $\operatorname{Ann}$ be the annulus semigroup and let … be the stated central extension. Diffeological universality conjecture. This extension is a universal central extension…

Universality conjecture. This central extension is a universal central extension. The claim concerns universality in the category of central extensions of the annulus semigroup. Th…

Let $M$ be a smooth manifold with volume form $\mu$, and let $\mathfrak{X}_{\mathrm{ex}}(M,\mu)$ be the Lie algebra of exact divergence-free vector fields. Consider the central ext…

Berarducci–Peterzil–Pillay's conjecture. The natural inclusion

Let $F$ be a field of characteristic different from $2$. Let $J$ be a Jordan algebra over $F$ generated by idempotents, and let a $\mathcal{J}(\frac{1}{2})$-axial central extension…

Let $\mathcal{S}$ be the Lie algebra in the paper, let $\mathcal{K}$ be its central module, and let a $\mathcal{K}$-valued affine cocycle be a bilinear map on $\mathcal{S}$ satisfy…