5 problems

Let ${p\mathcal{A}ss}^n_d$ be the operad for degree-$d$ partially associative $n$-ary algebras, in the non-Koszul parity case $n \not\equiv d \pmod{2}$. A gap in a minimal model me…

Let ${p\mathcal{A}ss}^n_d$ be the operad for degree-$d$ partially associative $n$-ary algebras. The Koszul duality isomorphisms identify ${p\mathcal{A}ss}^n_d$ with the Koszul dual…

Let ${t\mathcal{A}ss}^n_d$ be the operad for degree-$d$ totally associative $n$-algebras. The Koszul property is considered for arbitrary arity $n$ and degree $d$. Koszulity parity…

Finite-generation conjecture. Every polynomial identity satisfied by $n$-ary intermolecular recombination, with no restriction on the degree, is a consequence of complete symmetry…

Degree-$2n-1$ consequence conjecture. Every polynomial identity satisfied by $n$-ary intermolecular recombination in degree $2n-1$ is a consequence of complete symmetry in degree…