5 problems

Let $\mathfrak A$ be an associative algebra with a trace, and let $D_1,\dots,D_i$ be trace-preserving associative derivations satisfying conditions (i)--(iii): each $D_j$ is trace-…

Let $\mathrm{Vect}(\mathbb R^n)$ be the Lie algebra of vector fields on $\mathbb R^n$, let $\Omega(\mathbb R^n)$ denote the space of differential forms, and let…

Lie-algebra cohomology conjecture. (a) If

Let $L$ be a finite-dimensional nilpotent Lie algebra defined over the rational numbers, and let $C(L)$ denote its center. Nilpotent Lie algebra toral rank conjecture. Then … This…

Commutative 2-cocycle conjecture. The space of commutative $2$-cocycles on $L$ coincides with the space of symmetric bilinear invariant forms and is therefore $1$-dimensional, assu…