4 problems

Let $A_n$ be the free associative algebra on generators $x_1,\dots,x_n$, regarded as a Lie algebra with bracket $[a,b]=a\cdot b-b\cdot a$. Let $C^{\bullet}(A_n,A_n)$ be its Lie coc…

A differential graded Lie algebra $L$ is connected if it is concentrated in non-positive cohomological degrees, and its cohomology is nilpotent when it is nilpotent as a graded Lie…

Higher crossed-module conjecture. The differential $d$ gives $L$ the structure of an $n$-cat-group $\mathcal{C}(L)$, in the sense of Loday, and the geometrical realization…

Frégier's conjecture. Similar theories should exist for most algebraic structures, with a unified treatment based on differential graded Lie algebras.