4 problems

Let ${\cal C}(G)$ be the refined dihedral Lie coalgebra for a finite commutative group $G$, let ${C}_{\bullet}(G)$ be its graded dual, and let ${\rm Gr}^W{\cal G}^{(l)}$ be the wei…

Let $p$ be a prime number, let $\boldsymbol{}[p]$ be the group of $p$-th roots of unity, let ${D}^{\Delta}_{\bullet}(\boldsymbol{}[p])$ be the diagonal, depth-equals-weight part of…

Let ${D}_{\bullet \bullet}:={D}_{\bullet \bullet}(\{e\})$ be the dihedral Lie algebra for the trivial group, let $\xi=\xi_{\{e\}}$ be its embedding, and let…

Let $N$ be a positive integer, let $\boldsymbol{}[N]$ denote the group of $N$-th roots of unity, let ${\rm Gr}{\cal G}_{\bullet \bullet}^{(l)}(\boldsymbol{}[N])$ be the associated…