5 problems

Let $V^\bullet[\cdot]$ be a topological vertex operator algebra (TVOA), with dot product and bracket product defined by the vertex-operator operations above. The homotopy Gerstenha…

Extension property converse. If every $(S,\underline D)$-diagram of ${\cal P}$-algebras can be extended to an $S$-diagram of ${\cal P}$-algebras, then the couple $(S,D)$ has the…

Lian–Zuckerman's lifting conjecture. The product and bracket extend to a $G_\infty$ structure on $V$. The conjecture is presented as an open problem in the source, with no resoluti…

Open-closed Deligne conjecture. For any open-closed homotopy algebra $(\mathfrak l,\mathfrak q)$, there is a $G_\infty$ algebra structure on the space…

Jordan triple-system conjecture. There is an isomorphism