23 problems

Let $A$ be a Frobenius algebra, and let $C^\bullet(A,A)$ denote its Hochschild cochain complex. Framed Deligne conjecture. The framed little discs operad acts on $C^\bullet(A,A)$.…

Dual-basis conjecture. The elements $i_{(1)}\oB i_{(2)}$ form a dual basis for the Frobenius homomorphism $\Fi_B$. This conjecture is suggested by the corresponding double-algebra…

Cohomological-field-theory deformation conjecture. The non-degenerate part of the cohomological field theory described by $f$ is the deformation of the Frobenius algebra of the inv…

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

Deformation conjecture. The resulting theory is the deformation of the dual of the orbifold of the singularity with respect to the group $H$.

Completeness conjecture. Conversely, every CFT built from conformal blocks of the rational vertex algebra ${\mathfrak V}$ defined on world sheets of types (3) and (4) can be obtain…

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…

In a higher-dimensional setting, consider a separable algebra and the unitarity and Frobenius conditions on an algebraic structure of this kind. Higher-dimensional structure conjec…

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

Shimizu's conjecture. Every simple algebra in a finite tensor category is quasi-Frobenius.

CLS conjecture. For the Kodaira–Spencer map to be an isomorphism of Frobenius algebras, the residue pairing should be modified by a constant equal to the ratio of the Floer volume…

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…

Let $(Q,D_Q)$ be a decorated quiver, with vertex algebras and arrow bimodules obtained through flat Frobenius degenerations of decorations of an ordinary quiver. Let $\Pi_k(Q,D_Q)$…

Let $G \in \operatorname{Rep}(\mathcal{V})$ be a projective generator and set … Let $S_{\mathcal{V}}$ be the automorphism of $C(E)$ induced by the modular $S$-transformation, let…

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…

Let $M$ be a 1-connected closed oriented formal manifold of dimension $d$, and let $A$ be a commutative differential graded Poincaré duality algebra weakly equivalent to the de Rha…

A commutative Frobenius algebra is an algebraic structure with a commutative multiplication and a compatible nondegenerate Frobenius pairing. The Gauge/Bethe correspondence relates…

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…

Let $(A,E)$ be a commutative Frobenius pair over $k$. Let ${\bf FP}(A,E)$ be the subcategory of ${\rm Mod}_k$ whose objects are generated by $A^{\otimes m}\otimes E^{\otimes n}$ fo…

Small Frobenius functional conjecture. Every saturated Frobenius subalgebra of ${\operatorname{sl}}(n)$ has a small Frobenius functional.