14 problems

Stiénon–Xu conjecture. For every transitive Courant algebroid, there is an isomorphism between its standard cohomology and its naive cohomology.

Adjoint-cohomology vanishing conjecture. The adjoint cohomology vanishes in every positive degree:

Splitting conjecture. The algebra $L$ decomposes as

Let $\mathfrak{g}$ be a free Leibniz algebra, and let $\mathsf{Lie}(s\mathfrak{g})$ denote the Pirashvili complex with its Leibniz differential. Pirashvili's conjecture. The homolo…

Let $L$ be a solvable Leibniz algebra with a given nilradical, and suppose that the dimension of a complementary space to the nilradical is maximal. Maximal-complement conjecture.…

An embedding tensor on a Lie algebra representation $(\mathfrak g,V)$ is a linear map $T:V\to\mathfrak g$ satisfying the quadratic equivariancy constraint defining an embedding ten…

Vanishing conjecture. If ${\bf h}$ is a free Leibniz algebra, then

Vanishing conjecture.

The paper studies ${\mathcal{O}}$-operators on Leibniz algebras and Lie algebras. Extension conjecture. This theory should extend to algebras over Koszul operads. Such an extension…

Let $n\ge 2$, and consider an irreducible component of the variety of $n$-dimensional Leibniz algebras. Vergne–Grunewald–O'Halloran conjecture. Every such irreducible component con…

Conjecture. One has

Let $L$ be a Leibniz algebra, let $L/I$ be its corresponding Lie algebra, and let $I$ denote the ideal generated by squares of elements of $L$. Decomposition conjecture. Any Leibni…

Let $N_n$ denote the adapted number of isomorphism classes of $n$-dimensional non-Lie complex filiform Leibniz algebras in $SLeib_n$. Conjecture. The number $N_n$ is given by … The…

Let $N_n$ denote the number of isomorphism classes of $n$-dimensional none Lie complex filiform Leibniz algebras in $FLeib_n$. The classification in dimension $8$ gives $N_8=25$. C…