9 problems

Let $\mathfrak{g}$ and $\mathfrak{n}$ be Lie algebras, with $\mathfrak{g}$ reductive and $\mathfrak{n}$ semisimple. Suppose that the pair $(\mathfrak{g},\mathfrak{n})$ admits a pos…

Uri multiplicity threshold shuffle conjecture. The uri multiplicities satisfy the threshold shuffle identities from the source's definition. The supplied text gives no resolution s…

Let $\mathfrak{g}$ and $\mathfrak{n}$ be Lie algebras, and suppose that $\mathfrak{g}$ is perfect but not semisimple. Consider the three cases in which $\mathfrak{n}$ is nilpotent,…

Injectivity conjecture. The associated operad morphism from the operad of post-Lie algebras into the operad of opposite $\boldsymbol{\Phi}$-associative algebras is injective.

Let $F_{g,c}$ be the free-nilpotent Lie algebra with $g\ge 2$ generators and nilpotency class $c\ge 3$. A CPA-structure is central when its products take values in the center of…

Let $F_{g,c}$ be the free-nilpotent Lie algebra with $g$ generators and nilpotency class $c$, where $g\ge 2$ and $c\ge 2$. A central CPA-structure is a CPA-structure whose products…

Let $\mathfrak{g}$ be a nilpotent Lie algebra without an abelian factor, and let a CPA-structure on $\mathfrak{g}$ be a commutative post-Lie algebra structure with left and right m…

CPA-structure conjecture. Every CPA-structure on a complex perfect Lie algebra is trivial.

Let $\mathfrak{g}$ be a perfect Lie algebra, meaning $[\mathfrak{g},\mathfrak{g}]=\mathfrak{g}$. A commutative post-Lie algebra structure on $\mathfrak{g}$ is a commutative bilinea…