9 problems

Degenerate Frobenius structure conjecture. There is a degenerate $G$-Frobenius algebra of degree $j$ on the dual of a $G$-Euler $G$-Frobenius algebra.

Let $\mathbf{Caus}$ be the category of finite acyclic directed graphs equipped with a chosen topological order, with order-preserving graph homomorphisms or refinements as morphism…

Let the BrainiaK crystal space denote the semantic state space equipped with maps induced by semantic composition and tree decomposition. A finite-dimensional quotient or completio…

Let $(W,S)$ be a Coxeter system, let $\mathcal{H}$ be a two-sided cell, and let $d$ be a Duflo involution in $\mathcal{H}$ with $\mathtt{a}(d)=a$. Let $\widetilde{\mathrm{C}}_d$ be…

Converse characterization conjecture. If $(\mathfrak{I}_{\hat\Psi},\mathfrak{t}_{\hat\Psi})$ is a commutative Frobenius algebra in

Uniqueness conjecture. Non-degenerate standard A-H Frobenius monoids differ only by their scalars. More precisely, but less generally, all non-abelian simple A-H F. monoids are iso…

Finite-dimensional Frobenius algebra conjecture. Then $A$ admits a unit for $\mu$ and a counit for $\delta$, and is, in fact, a Frobenius algebra.

Let $R$ be a Frobenius algebra with an ideal $\mathfrak m$ such that … and let $B$ and $B'$ be forms on $R$ related by $B'(r,s)=B(r,su)$ for some $u\in U(R)$. Suppose that $B$ has…

Finite-generation converse conjecture. If the order of the canonical module is a multiple of the characteristic of $R$, then $\mathcal F(E)$ is not a finitely generated ring extens…