11 problems

Let $R\subset\mathrm{Cend}_N$ be a subalgebra acting irreducibly on the free $\mathbb{C}[\partial]$-module $\mathbb{C}[\partial]^N$. Let $\mathrm{Cur}(\mathrm{Mat}_N\mathbb{C})$ de…

Let $C$ be a finitely generated simple associative conformal algebra of Gel'fand–Kirillov dimension one. For $Q\in M_N(\Bbbk[v])$ with $\det Q\ne0$, let…

Let $C$ be a conformal algebra and let $I_1\subseteq I_2\subseteq\dots$ be an ascending chain of nilpotent ideals of $C$. Denote by $n_j$ the nilpotency index of $I_j$. Nilpotency-…

Let $\Bbbk$ be an algebraically closed field of characteristic zero, let $H=\Bbbk[D]$, and let $V_N$ be the free $N$-generated $H$-module. Write…

An associative conformal algebra is annihilation-free if it has no nonzero annihilator, in the sense explained in the cited reference. A differential conformal algebra is an associ…

Let $\Bbbk$ be an algebraically closed field of characteristic zero, let $H=\Bbbk[D]$, and let $V_N$ be the free $N$-generated $H$-module. Write…

Let $C$ be an associative conformal algebra that is $\partial$-torsion free, meaning that no nonzero element of $C$ is annihilated by a nonzero polynomial in $\partial$. A unital c…

Let $N$ be a positive integer. The associative conformal algebra $\Cend_N$ acts on $\mathbb{C}[\partial]^N$, and a subalgebra is irreducible if its action on this module is irreduc…

Conjecture. This associative conformal subalgebra is isomorphic to one of

Let ${\cal M}_p$ be the matrix of all Shapovalov forms at grade $p$, let $m$ and $\Delta$ denote the parameters appearing in these forms, and write $\left[\frac{p}{2}\right]$ for t…

Let $H=\Bbbk[T]$, and let $L$ be a finite Lie conformal algebra that is torsion-free as an $H$-module. An embedding conjecture. $L$ can be embedded into an associative conformal al…