4 problems

Let $\mathfrak{g}$ be a non-trivial finite-dimensional complex Lie algebra. Say that $\mathfrak{g}$ satisfies the Pirashvili conditions if, equivalently, $HL_p(\mathfrak{g})=0$ for…

Let $R$ be a unital associative ring and let $\mathrm{GL}(R)$ denote its infinite linear group. Write $\mathrm{HL}_{\bullet}(\mathrm{GL}(R),\Bbbk)$ for the Leibniz homology of this…

Let $G$ be an abelian group, let $\Bbbk$ be a field, let $\mathrm{HL}_n(G,\Bbbk)$ denote Leibniz homology, and let $\mathrm{H}_n(G,\Bbbk)$ denote Eilenberg–MacLane homology. Write…

Let $\mathbf{Grp}$ be the category of groups, let $\mathbf{Zinb}^c$ denote coZinbiel coalgebras, and let $\mathbf{Com}^c$ denote cocommutative coalgebras. For a group $G$, write…